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{"sheet":"Tools","index":0,"n_rows":32,"n_cols":5,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[null,"EXCEL PROJECT"]
[]
[null,"Fonction ","Calcul","Entrée","Sortie"]
[]
[null,"MTran(M)","Transpose la matrice","Matrice ou Vecteur","Matrice ou Vecteur"]
[null,"MInverse(M)","Inverse la matrice","Matrice carrée nxn","Matrice carrée nxn"]
[null,"MProd(Mx, My)","Produit matriciel","2 Matrices compatibles","Matrice ou Nombre"]
[null,"MTProd(Mx, My)","Produit transposée x matrice: tMx My","2 Matrices compatibles","Matrice ou Nombre"]
[null,"MSProd(Mx)","Produit transposée x matrice: tMx Mx","1 Matrices compatibles","Matrice ou Nombre"]
[null,"MQProd(Mx, My)","Produit quadratique: tMx My Mx","2 Matrices compatibles","Nombre"]
[null,"MQProdD(Mx, My)","Produit quadratique: Mx My inv(Mx)","2 Matrices compatibles","Nombre"]
[null,"MQProdG(Mx, My)","Produit quadratique: inv(Mx) My Mx","2 Matrices compatibles","Nombre"]
[null,"MZero(n,m)","Matrice Zero","Tailles n et m ","Matrice nxm"]
[null,"MUn(n)","Matrice Identité","Taille n","Matrice unitaire carrée nxn"]
[null,"MScal(n,k)","Matrice Scalaire de diagonale k","Taille n et k","Matrice diagonale carrée nxn"]
[null,"MDiagVP(P)","Matrice diagonale quelconque","Vecteur Colonne","Matrice diagonale nxn"]
[null,"MAdd(M,k)","Addition d'un nombre à une matrice","Matrice nxm et k","Matrice nxm"]
[null,"MMul(M,k)","Multiplication d'un nombre par une matrice","Matrice nxm et k","Matrice nxm"]
[]
[null,"MCentre(M)","Matrice Centrée","Matrice carrée nxm","Matrice carrée nxm"]
[null,"MReduit(M)","Matrice Centrée Réduite","Matrice carrée nxm","Matrice carrée nxm"]
[null,"MCovariance(M)","Matrice de Covariance de M","Matrice carrée nxm","Matrice carrée symétrique mxm"]
[null,"MCorrelation(M)","Matrice de Corrélation de M","Matrice carrée nxm","Matrice carrée symétrique mxm"]
[null,"MCholesky(M)","Matrice \"Racine Carrée\" de Cholesky ","Matrice carrée nxn","Matrice carrée triangulaire inférieure nxn"]
[]
[null,"ValP(M)","Valeurs Propres de M","Matrice carrée nxn","Vecteur horizontal n"]
[null,"VecP(M)","Vecteurs Propres de M","Matrice carrée nxn","Matrice carrée nxn"]
[]
[null,"NHalton(p,k)","Nombres de Halton","Base (p) er Rang (k)","Nombre"]
[null,"TPascal(n,k)","Triangle de Pascal","Ligne (n) Colonne (k)","Coefficient du binome (n,k)"]
[null,"TCatalan(n,k)","Triangle de Catalan","Ligne (n) Colonne (k)","Nombre de TCatalan (n,k)"]
[null,"NCatalan(k)","Nombres de Catalan","Rang k","Nombre de Catalan (k) = TCatalan(k,kà"]

{"sheet":"ExoCorrec1","index":1,"n_rows":93,"n_cols":17,"rows_kept":93,"cut":false,"hidden":true,"merged":[]}
["MATRICES Exercices - Application avec Autocorrection"]
[]
[]
["ADDITION DE DEUX MATRICES"]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,"A+B"]
[null,15,-85,0,null,8,78,0,"OK",null,null,{"$f":"B6:D9+F6:H9","v":23},-7,0,{"$f":"form(L6)","v":"=B6:D9+F6:H9"}]
[null,0,55,6,null,88,0,6,null,null,null,88,55,12]
[null,-7,0,-33,null,4,1,5,null,null,null,-3,1,-28]
[null,2,-4,8,null,-7,-22,-77,null,null,null,-5,-26,-69]
[]
["MULTIPLICATION PAR UN NOMBRE"]
[null,"matrice A",null,null,null,"scalaire b",null,null,null,null,null,"A.b"]
[null,15,-85,0,null,8,null,null,"OK",null,null,{"$f":"B13:D16*F13","v":120},-680,0,{"$f":"form(L13)","v":"=B13:D16*F13"}]
[null,0,55,6,null,null,null,null,null,null,null,0,440,48]
[null,-7,0,-33,null,null,null,null,null,null,null,-56,0,-264]
[null,2,-4,8,null,null,null,null,null,null,null,16,-32,64]
[]
["DETERMINANT D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"determinant (A)"]
[null,15,-85,0,5,null,null,null,"OK",null,null,{"$f":"MDETERM(B20:E23)","v":-212325},null,null,{"$f":"form(L20)","v":"=DETERMAT(B20:E23)"}]
[null,0,55,6,1]
[null,-7,0,-33,8]
[null,2,-4,8,7]
[]
["TRANSPOSEE D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"AT"]
[null,15,-85,0,null,null,null,null,"OK",null,null,{"$f":"TRANSPOSE(B27:D30)","v":15},0,-7,2,null,{"$f":"form(N27)","v":"=TRANSPOSE(B27:D30)"}]
[null,0,55,6,null,null,null,null,null,null,null,-85,55,0,-4]
[null,-7,0,-33,null,null,null,null,null,null,null,0,6,-33,8]
[null,2,-4,8]
[]
["PRODUIT DE DEUX MATRICES"]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,"A.B"]
[null,15,-85,0,null,8,78,0,"OK",null,null,{"$f":"MMULT(B34:D37,F34:H36)","v":-7360},1170,-510,{"$f":"form(L34)","v":"=PRODUITMAT(B34:D37;F34:H36)"}]
[null,0,55,6,null,88,0,6,null,null,null,4864,6,360]
[null,-7,0,-33,null,4,1,5,null,null,null,-188,-579,-165]
[null,2,-4,8,null,null,null,null,null,null,null,-304,164,16]
[]
["INVERSE D'UNE MATRICE"]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"A-1"]
[null,15,-85,0,null,null,null,null,"OK",null,null,{"$f":"MINVERSE(B41:D43)","v":4.8168789808917208E-2},7.444267515923568E-2,1.353503184713376E-2,{"$f":"form(L41)","v":"=INVERSEMAT(B41:D43)"}]
[null,5,55,6,null,null,null,null,null,null,null,-3.2643312101910825E-3,1.3136942675159238E-2,2.3885350318471341E-3]
[null,-7,0,-33,null,null,null,null,null,null,null,-1.0217622080679408E-2,-1.5790870488322718E-2,-3.3174097664543524E-2]
[]
["PRODUIT SCALAIRE"]
[null,"vecteur A",null,null,null,null,"vecteur B",null,null,null,null,"A.B"]
[null,15,8,-7,14,null,1,null,"OK",null,null,{"$f":"MMULT(B47:E47,G47:G50)","v":22},null,null,{"$f":"form(L47)","v":"=PRODUITMAT(B47:E47;G47:G50)"}]
[null,null,null,null,null,null,0]
[null,null,null,null,null,null,5]
[null,null,null,null,null,null,3]
[]
["PRODUIT D'UNE MATRICE ET DE SA TRANSPOSEE"]
[]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"A.AT"]
[null,15,-85,0,null,null,null,null,"OK",null,null,{"$f":"MMULT(B55:D57,TRANSPOSE(B55:D57))","v":7450},-4600,-105,{"$f":"form(L55)","v":"=PRODUITMAT(B55:D57;TRANSPOSE(B55:D57))"}]
[null,5,55,6,null,null,null,null,null,null,null,-4600,3086,-233]
[null,-7,0,-33,null,null,null,null,null,null,null,-105,-233,1138]
[]
[null,null,null,null,null,null,null,null,null,null,null,"AT.A"]
[null,null,null,null,null,null,null,null,"OK",null,null,{"$f":"MMULT(TRANSPOSE(B55:D57),B55:D57)","v":299},-1000,261,{"$f":"form(L60)","v":"=PRODUITMAT(TRANSPOSE(B55:D57);B55:D57)"}]
[null,null,null,null,null,null,null,null,null,null,null,-1000,10250,330]
[null,null,null,null,null,null,null,null,null,null,null,261,330,1125]
[]
["RESOLUTION D'UN SYSTEME D'EQUATIONS"]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"A-1,x"]
[null,13,"a               +",-8,"b               +",-3,"c               =",20,"OK",null,null,"a=",{"$f":"MMULT(MINVERSE(D77:F79),H77:H79)","v":3},null,{"$f":"form(M73)","v":"=PRODUITMAT(INVERSEMAT(D77:F79);H77:H79)"}]
[null,-8,"a               +",10,"b               +",-1,"c               =",-5,null,null,null,"b=",2.0000000000000004]
[null,-3,"a               +",-1,"b               +",11,"c               =",0,null,null,null,"c=",0.99999999999999989]
[null,null,null,null,null,null,null,null,null,null,null,"vérification","A,x"]
[null,"premier membre: A",null,13,-8,-3,"sec membre: B",20,"OK",null,null,null,{"$f":"MMULT(D77:F79,M73:M75)","v":19.999999999999996},null,{"$f":"form(M77)","v":"=PRODUITMAT(D77:F79;M73:M75)"}]
[null,null,null,-8,10,-1,null,-5,null,null,null,null,-4.9999999999999964]
[null,null,null,-3,-1,11,null,0,null,null,null,null,-1.7763568394002505E-15]
[]
["CALCUL DE LA TRACE D'UNE MATRICE CARREE"]
[]
[null,"matrice A",null,null,null,null,null,null,null,null,null,"trace (A)"]
[null,15,-85,0,null,null,null,null,"OK",null,null,{"$f":"SUM(B84:D86*MMULT(B84:D86,MINVERSE(B84:D86)))","v":37},null,null,{"$f":"form(L84)","v":"=SOMME(B84:D86*PRODUITMAT(B84:D86;INVERSEMAT(B84:D86)))"}]
[null,5,55,6]
[null,-7,0,-33]
[]
["CALCUL DE LA TRACE DU PRODUIT DE DEUX MATRICES CARREES"]
[]
[null,"matrice A",null,null,null,"matrice B",null,null,null,null,null,"trace (AB)"]
[null,15,-85,0,null,12,2,23,"OK",null,null,{"$f":"SUM((B91:D93*TRANSPOSE(F91:H93)))","v":2754},null,null,{"$f":"form(L91)","v":"=SOMME((B91:D93*TRANSPOSE(F91:H93)))"}]
[null,5,55,6,null,-34,0,5,null,null,null,"trace (BA)"]
[null,-7,0,-33,null,38,-11,3,"OK",null,null,{"$f":"SUM((TRANSPOSE(B91:D93)*(F91:H93)))","v":2754},null,null,{"$f":"form(L93)","v":"=SOMME((TRANSPOSE(B91:D93)*(F91:H93)))"}]

{"sheet":"Matrice","index":2,"n_rows":83,"n_cols":6,"rows_kept":83,"cut":false,"hidden":false,"merged":[]}
["FONCTIONS MATRICIELLES"]
[]
[null,"Matrice Mx"]
[null,15,-85,0,-20]
[null,3,55,6,55]
[null,-7,1,-33,0]
[null,2,-4,8,4]
[]
[null,"Inverse de la matrice"]
[null,{"$f":"_xludf.Minverse($B$4:$E$7)","v":7.069319833592301E-2},6.8668237181093675E-2,-0.1307202646483886,-0.59072226956042329,{"$f":"form(B10)","v":"=Minverse($B$4:$E$7)"}]
[null,1.6139541877600127E-3,1.0926770587940456E-2,-3.2479574958648699E-2,-0.14217332464538124]
[null,-1.4946619217081852E-2,-1.4234875444839857E-2,-3.5587188612099577E-3,0.12099644128113882]
[null,-3.8394065460377936E-3,5.0624028870733277E-3,3.9997995087965532E-2,0.16119492757255283]
[null,"Transpose de la matrice"]
[null,{"$f":"MTran($B$4:$E$7)","v":15},3,-7,2,{"$f":"form(B15)","v":"=MTran($B$4:$E$7)"}]
[null,-85,55,1,-4]
[null,0,6,-33,8]
[null,-20,55,0,4]
[null,"Produit de 2 matrices: Mx My"]
[null,{"$f":"MProd($B$4:$E$7,$B$4:$E$7)","v":-70},-5870,-670,-5055,{"$f":"form(B20)","v":"=MProd($B$4:$E$7;$B$4:$E$7)"}]
[null,278,2556,572,3185]
[null,129,617,1095,195]
[null,-30,-398,-256,-244]
[null,"Produit de 2 matrices: t(Mx) My"]
[null,{"$f":"MTProd($B$4:$E$7,$B$4:$E$7)","v":287},-1125,265,-127,{"$f":"form(B25)","v":"=MTProd($B$4:$E$7;$B$4:$E$7)"}]
[null,-1125,10267,265,4709]
[null,265,265,1189,362]
[null,-127,4709,362,3441]
[null,"Produit scalaire: t(Mx) Mx"]
[null,{"$f":"MSProd($B$4:$E$7)","v":287},-1125,265,-127,{"$f":"form(B30)","v":"=MSProd($B$4:$E$7)"}]
[null,-1125,10267,265,4709]
[null,265,265,1189,362]
[null,-127,4709,362,3441]
[null,"Produit quadratique 2 matrices: t(Mx) My Mx"]
[null,{"$f":"MQProd($B$4:$E$7,$B$4:$E$7)","v":-1179},-85497,-16511,-68123,{"$f":"form(B35)","v":"=MQProd($B$4:$E$7;$B$4:$E$7)"}]
[null,21489,641739,90529,606021]
[null,-2829,-8209,-34751,10723]
[null,16570,256388,43836,275299]
[null,"Produit quadratique 2 matrices: inv(Mx) My Mx"]
[null,{"$f":"MQProdG($B$4:$E$7,$B$4:$E$7)","v":15.000000000000002},-84.999999999999957,-1.7763568394002505E-15,-19.999999999999954,{"$f":"form(B40)","v":"=MQProdG($B$4:$E$7;$B$4:$E$7)"}]
[null,3.0000000000000013,55,6.0000000000000053,55]
[null,-7,1.0000000000000016,-33,1.4432899320127035E-15]
[null,1.9999999999999978,-4.0000000000000187,7.9999999999999929,3.9999999999999827]
[null,"Produit quadratique 2 matrices: Mx My inv(Mx)"]
[null,{"$f":"MQProdD($B$4:$E$7,$B$4:$E$7)","v":15.000000000000002},-85,0,-20,{"$f":"form(B45)","v":"=MQProdD($B$4:$E$7;$B$4:$E$7)"}]
[null,3,55,6.0000000000000142,55.000000000000057]
[null,-7.0000000000000036,1.0000000000000013,-33,-1.0658141036401503E-14]
[null,2,-3.9999999999999996,7.9999999999999982,4.0000000000000142]
[]
[null,"Addition à 1 matrice d'un scalaire: Mx + N ",null,null,10]
[null,{"$f":"MAddScal($B$4:$E$7,E50)","v":25},-75,10,-10,{"$f":"form(B51)","v":"=MAddScal($B$4:$E$7;E50)"}]
[null,13,65,16,65]
[null,3,11,-23,10]
[null,12,6,18,14]
[null,"Produit de 1 matrice par un scalaire: Mx . N ",null,null,10]
[null,{"$f":"MMulScal($B$4:$E$7,E55)","v":150},-850,0,-200,{"$f":"form(B56)","v":"=MMulScal($B$4:$E$7;E55)"}]
[null,30,550,60,550]
[null,-70,10,-330,0]
[null,20,-40,80,40]
[]
[null,"Matrice zero"]
[null,{"$f":"MZero(4,4)","v":0},0,0,0,{"$f":"form(B62)","v":"=MZero(4;4)"}]
[null,0,0,0,0]
[null,0,0,0,0]
[null,0,0,0,0]
[]
[null,"Matrice Identité"]
[null,{"$f":"MUn(4)","v":1},0,0,0,{"$f":"form(B68)","v":"=MUn(4)"}]
[null,0,1,0,0]
[null,0,0,1,0]
[null,0,0,0,1]
[]
[null,"Matrice Scalaire"]
[null,{"$f":"MScal(4,5)","v":5},0,0,0,{"$f":"form(B74)","v":"=MScal(4;5)"}]
[null,0,5,0,0]
[null,0,0,5,0]
[null,0,0,0,5]
[]
[null,"Matrice Diag"]
[null,{"$f":"MDiag(B4:B7)","v":15},0,0,0,{"$f":"form(B80)","v":"=MDiag(B4:B7)"}]
[null,0,3,0,0]
[null,0,0,-7,0]
[null,0,0,0,2]

{"sheet":"Covariance","index":3,"n_rows":63,"n_cols":8,"rows_kept":63,"cut":false,"hidden":false,"merged":[]}
["FONCTIONS MCENTRE MREDUITE MCOVARIANCE MCORRELATION"]
["MATRICE DE COVARIANCE, MATRICE DE CORRELATION"]
[null,"Matrice Entrée"]
[null,null,1,2,3,4,5]
[null,1,1.0439000000000001,0.83889999999999998,1.0750999999999999,123.38,9.0623000000000005]
[null,2,1.0422,0.84140000000000004,1.0709,122.19,9.0485000000000007]
[null,3,1.0364,0.83977999999999997,1.0687,122.43,9.0343]
[null,4,1.0421,0.84240000000000004,1.0689,122.31,9.0259999999999998]
[null,5,1.0444,0.84645000000000004,1.0706,122.86,9.0975000000000001]
[null,6,1.0446,0.85277999999999998,1.0710999999999999,122.6,9.0928000000000004]
[null,7,1.0445,0.85299999999999998,1.0753999999999999,122.61,9.1077999999999992]
[null,8,1.0401,0.85128000000000004,1.0713999999999999,122.39,9.0777000000000001]
[null,9,1.0452999999999999,0.85299999999999998,1.0713999999999999,122.04,9.0757999999999992]
[null,10,1.0541,0.85618000000000005,1.0739000000000001,123.4,9.0862999999999996]
[null,"Calculs intermédiaires:"]
[null,"MOYENNE",{"$f":"AVERAGE(C5:C14)","v":1.04376},{"$f":"AVERAGE(D5:D14)","v":0.84751700000000008},{"$f":"AVERAGE(E5:E14)","v":1.0717400000000001},{"$f":"AVERAGE(F5:F14)","v":122.62100000000001},{"$f":"AVERAGE(G5:G14)","v":9.0708999999999982},{"$f":"form(C16)","v":"=MOYENNE(C5:C14)"}]
[null,"ECART TYPE",{"$f":"STDEVP(C5:C14)","v":4.2863037689832512E-3},{"$f":"STDEVP(D5:D14)","v":6.130964116678554E-3},{"$f":"STDEVP(E5:E14)","v":2.2204504047602575E-3},{"$f":"STDEVP(F5:F14)","v":0.4416435214061214},{"$f":"STDEVP(G5:G14)","v":2.6052792556652989E-2},{"$f":"form(C17)","v":"=ECARTYPEP(C5:C14)"}]
[null,"Matrice Centrée"]
[null,null,{"$f":"mcentre(MATAA)","v":1.4000000000002899E-4},-8.6170000000000968E-3,3.3599999999998076E-3,0.75899999999998613,-8.5999999999977206E-3,{"$f":"form(C19)","v":"=mcentre(MATAA)"}]
[null,null,-1.5600000000000058E-3,-6.1170000000000391E-3,-8.4000000000017394E-4,-0.4310000000000116,-2.2399999999997533E-2]
[null,null,-7.3600000000000332E-3,-7.7370000000001049E-3,-3.0400000000001537E-3,-0.1910000000000025,-3.659999999999819E-2]
[null,null,-1.6599999999999948E-3,-5.1170000000000382E-3,-2.8400000000001757E-3,-0.31100000000000705,-4.4899999999998386E-2]
[null,null,6.3999999999997392E-4,-1.0670000000000401E-3,-1.1400000000001409E-3,0.23899999999999011,2.6600000000001955E-2]
[null,null,8.399999999999519E-4,5.2629999999999066E-3,-6.4000000000019597E-4,-2.1000000000015007E-2,2.1900000000002251E-2]
[null,null,7.3999999999996291E-4,5.4829999999999046E-3,3.6599999999997745E-3,-1.1000000000009891E-2,3.6900000000001043E-2]
[null,null,-3.6599999999999966E-3,3.7629999999999608E-3,-3.4000000000022901E-4,-0.23100000000000875,6.8000000000019156E-3]
[null,null,1.5399999999998748E-3,5.4829999999999046E-3,-3.4000000000022901E-4,-0.58100000000000307,4.9000000000010147E-3]
[null,null,1.0340000000000016E-2,8.6629999999999763E-3,2.1599999999999397E-3,0.77899999999999636,1.5400000000001413E-2]
[null,"Matrice de Covariance"]
[null,null,{"$f":"MCovariance(MATAA)","v":1.8372400000000024E-5},1.6581679999999952E-5,5.3366000000001303E-6,1.0833400000000118E-3,5.8226999999999102E-5,{"$f":"form(C30)","v":"=MCovariance(MATAA)"}]
[null,null,1.6581679999999952E-5,3.758872100000004E-5,4.7722199999999936E-6,1.4330300000000564E-4,1.1991199999999831E-4]
[null,null,5.3366000000001303E-6,4.7722199999999936E-6,4.9303999999999909E-6,6.0356000000000971E-4,3.4869999999999685E-5]
[null,null,1.0833400000000118E-3,1.4330300000000564E-4,6.0356000000000971E-4,0.19504899999999925,3.7152000000000001E-3]
[null,null,5.8226999999999102E-5,1.1991199999999831E-4,3.4869999999999685E-5,3.7152000000000001E-3,6.7874799999999335E-4]
[]
[null,null,{"$f":"MMULT(TRANSPOSE(MATAA-$C$16:$G$16),(MATAA-$C$16:$G$16))/ROWS(MATAA)","v":1.8372400000000024E-5},1.6581679999999952E-5,5.3366000000001295E-6,1.0833400000000118E-3,5.8226999999999095E-5,{"$f":"form(C36)","v":"=PRODUITMAT(TRANSPOSE(MATAA-$C$16:$G$16);(MATAA-$C$16:$G$16))/LIGNES(MATAA)"}]
[null,null,1.6581679999999952E-5,3.758872100000004E-5,4.7722199999999936E-6,1.4330300000000564E-4,1.1991199999999831E-4]
[null,null,5.3366000000001295E-6,4.7722199999999936E-6,4.9303999999999909E-6,6.0356000000000971E-4,3.4869999999999685E-5]
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[null,null,5.8226999999999095E-5,1.1991199999999831E-4,3.4869999999999685E-5,3.7151999999999997E-3,6.7874799999999335E-4]
[null,"Matrice Réduite"]
[null,null,{"$f":"MReduit(MATAA)","v":3.2662174112312425E-2},-1.4054885717821921,1.5132065066311744,1.7185806271619133,-0.330098970428433,{"$f":"form(C42)","v":"=MReduit(MATAA)"}]
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[null,null,-1.7170971533326482,-1.261954865948572,-1.3690916012378769,-0.43247549379174671,-1.4048398043817734]
[null,null,-0.38728006447448016,-0.83461587812573401,-1.2790197853669785,-0.7041878459122225,-1.7234236944465158]
[null,null,0.14931279594196264,-0.17403461832327244,-0.5134093504642413,0.54116043463990482,1.0210037922557313]
[null,null,0.19597304467382273,0.85842942477538153,-0.28822981078699511,-4.7549661621115451E-2,0.84060086655643507]
[null,null,0.17264292030789269,0.89431285123378657,1.6483142304375222,-2.4906965611065073E-2,1.4163548847456686]
[null,null,-0.85388255179313288,0.61376969892262667,-0.15312208698064741,-0.52304627783191604,0.26100848824588041]
[null,null,0.35928391523533304,0.89431285123378657,-0.15312208698064741,-1.3155406381832611,0.18807964594187038]
[null,null,2.4123348594374359,1.4129914700416573,0.97277561140578361,1.7638660191820141,0.59110745867438153]
[null,"Matrice de Corrélation"]
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[null,null,0.63098176605476175,0.99999999999960854,0.35055051126954628,5.2924241678386032E-2,0.75072277394114784]
[null,null,0.56071300412446234,0.35055051126954628,1.0000000000804996,0.61547087811875001,0.60277688322535772]
[null,null,0.57228184509816116,5.2924241678386032E-2,0.61547087811875001,1.0000000000003739,0.32289108367563824]
[null,null,0.52141940195466907,0.75072277394114784,0.60277688322535772,0.32289108367563824,0.99999999993929567]
[]
[null,null,{"$f":"MMULT(TRANSPOSE((MATAA-C16:G16)/C17:G17),(MATAA-C16:G16)/C17:G17)/ROWS(MATAA)","v":0.99999999999999978},0.63098176605144674,0.56071300409883817,0.57228184509493552,0.52141940196765391,{"$f":"form(C59)","v":"=PRODUITMAT(TRANSPOSE((MATAA-C16:G16)/C17:G17);(MATAA-C16:G16)/C17:G17)/LIGNES(MATAA)"}]
[null,null,0.63098176605144674,1.0000000000000002,0.35055051125550535,5.2924241678386517E-2,0.7507227739640806]
[null,null,0.56071300409883817,0.35055051125550535,0.99999999999999978,0.61547087809386247,0.6027768832193916]
[null,null,0.57228184509493552,5.2924241678386517E-2,0.61547087809386247,1.0000000000000002,0.32289108368537833]
[null,null,0.52141940196765391,0.7507227739640806,0.6027768832193916,0.32289108368537833,0.99999999999999944]

{"sheet":"Cholesky","index":4,"n_rows":23,"n_cols":8,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["FONCTION CHOLESKY"]
["MATRICE DE CHOLESKY"]
[null,"Matrice Entrée"]
[null,null,1,2,3,4,5]
[null,1,0.99999999999999978,0.63098176605144674,0.56071300409883817,0.57228184509493552,0.52141940196765391]
[null,2,0.63098176605144674,1.0000000000000002,0.35055051125550535,5.2924241678386517E-2,0.7507227739640806]
[null,3,0.56071300409883817,0.35055051125550535,0.99999999999999978,0.61547087809386247,0.6027768832193916]
[null,4,0.57228184509493552,5.2924241678386517E-2,0.61547087809386247,1.0000000000000002,0.32289108368537833]
[null,5,0.52141940196765391,0.7507227739640806,0.6027768832193916,0.32289108368537833,0.99999999999999944]
[]
[null,"Matrice Sortie"]
[null,null,{"$f":"C4","v":1},{"$f":"D4","v":2},{"$f":"E4","v":3},{"$f":"F4","v":4},{"$f":"G4","v":5}]
[null,{"$f":"+B5","v":1},{"$f":"MCholesky(C5:G9)","v":0.99999999999999989},0,0,0,0,{"$f":"form(C13)","v":"=MCholesky(C5:G9)"}]
[null,{"$f":"+B6","v":2},0.63098176605144685,0.77579766106285564,0,0,0]
[null,{"$f":"+B7","v":3},0.56071300409883829,-4.1881672011493008E-3,0.82799962940206151,0,0]
[null,{"$f":"+B8","v":4},0.57228184509493563,-0.3972365258185897,0.35376985948949735,0.62413421541131242,0]
[null,{"$f":"+B9","v":5},0.52141940196765402,0.54359101608953331,0.37764134536741339,0.17116239525208352,0.5106085224505188]
[]
[null,null,{"$f":"MMULT(C13:G17,TRANSPOSE(C13:G17))-C5:G9","v":0},0,0,0,0]
[null,null,0,0,0,-2.0816681711721685E-17,1.1102230246251565E-16]
[null,null,0,0,0,0,0]
[null,null,0,-2.0816681711721685E-17,0,0,0]
[null,null,0,1.1102230246251565E-16,0,0,0]

{"sheet":"ValVecPropres","index":5,"n_rows":33,"n_cols":8,"rows_kept":33,"cut":false,"hidden":false,"merged":[]}
["FONCTIONS VALP et VECP"]
["VALEURS PROPRES ET VECTEURS PROPRES"]
[null,"Matrice Entrée"]
[null,null,1,2,3,4,5]
[null,1,1.8372400000000024E-5,1.6581679999999952E-5,5.3366000000001295E-6,1.0833400000000118E-3,5.8226999999999095E-5]
[null,2,1.6581679999999952E-5,3.758872100000004E-5,4.7722199999999936E-6,1.4330300000000564E-4,1.1991199999999831E-4]
[null,3,5.3366000000001295E-6,4.7722199999999936E-6,4.9303999999999909E-6,6.0356000000000971E-4,3.4869999999999685E-5]
[null,4,1.0833400000000118E-3,1.4330300000000564E-4,6.0356000000000971E-4,0.19504899999999922,3.7151999999999997E-3]
[null,5,5.8226999999999095E-5,1.1991199999999831E-4,3.4869999999999685E-5,3.7151999999999997E-3,6.7874799999999335E-4]
[]
[null,"Valeurs Propres"]
[null,null,{"$f":"MvalP(C5:G9)","v":0.19512799126343597},6.3434671366345921E-4,2.0571479961342754E-5,3.7536142804997724E-6,1.9764496579804553E-6,{"$f":"form(C12)","v":"=MvalP(C5:G9)"}]
[]
[null,"Vecteurs Propres"]
[null,null,{"$f":"Mvecp(C5:G9)","v":5.5571907995008215E-3},6.4042113413756666E-2,0.60358411003938084,0.75086877360914217,-0.26028836367880243,{"$f":"form(C15)","v":"=Mvecp(C5:G9)"}]
[null,null,7.4668847411716395E-4,0.19396319005940604,0.77357810796435988,-0.57370341114206791,0.18659858059625761]
[null,null,3.0961838486059344E-3,3.7682355708561065E-2,1.9760860434992378E-3,0.32298288332413183,0.94564718890155219]
[null,null,0.99979696436945487,-1.930607789525747E-2,-2.5024108422175913E-4,-5.740013267484796E-3,-5.4315836925529243E-4]
[null,null,1.9105071838105472E-2,0.97800010431289508,-0.19302633356513393,5.2053724074049394E-2,-5.6409543115072583E-2]
[]
[null,null,{"$f":"MMULT(C5:G9,C15:G19)","v":1.0843634777742432E-3},4.0624904180079058E-5,1.2416618424660021E-5,2.8184717514006283E-6,-5.1444684736926094E-7,{"$f":"form(C21)","v":"=PRODUITMAT(C5:G9;C15:G19)"}]
[null,null,1.4569982205404224E-4,1.2303991218586514E-4,1.5913646546522265E-5,-2.1534613168342975E-6,3.6880270079911441E-7]
[null,null,6.0415213496077037E-4,2.3903678506823203E-5,4.0651014445732304E-8,1.2123531632024528E-6,1.8690240630746519E-6]
[null,null,0.19508837332869275,-1.224674706658789E-5,-5.1478294498235461E-9,-2.1545795770997259E-8,-1.0735251730262501E-9]
[null,null,3.7279342907131602E-3,6.2039115213340535E-4,-3.9708373529465883E-6,1.9538960203756257E-7,-1.1149062219660967E-7]
[]
[null,null,{"$f":"C21/C15","v":0.195127991263436},{"$f":"D21/D15","v":6.3434671366345888E-4},2.0571479961342751E-5,3.7536142804997745E-6,1.9764496579804536E-6,{"$f":"form(C27)","v":"=C21/C15"}]
[null,null,{"$f":"C22/C16","v":0.19512799126343588},6.343467136634591E-4,2.0571479961342748E-5,3.7536142804997707E-6,1.9764496579804693E-6]
[null,null,0.195127991263436,6.3434671366345921E-4,2.057147996134207E-5,3.7536142804997715E-6,1.9764496579804553E-6]
[null,null,0.19512799126343591,6.3434671366348826E-4,2.0571479962345563E-5,3.753614280483774E-6,1.9764496577639541E-6]
[null,null,0.19512799126343591,6.3434671366345932E-4,2.0571479961342615E-5,3.753614280500079E-6,1.9764496579802906E-6]
[]
[null,null,{"$f":"C27-C12","v":0},{"$f":"D27-D12","v":0},0,0,0,{"$f":"SUM(C33:G33)","v":0}]

{"sheet":"ExoCorrec2","index":6,"n_rows":91,"n_cols":13,"rows_kept":91,"cut":false,"hidden":true,"merged":[]}
["MATRICES Exercices"]
[]
[]
["CALCUL DU PRODUIT MATRICIEL D'UNE MATRICE PAR SA TRANSPOSEE",null,null,null,null,null,"On obtient une matrice symétrique"]
[]
[]
[null,11,3,5,8,null,null,null,null,{"$f":"MMULT(B7:E10,TRANSPOSE(B7:E10))","v":219},69,-176,255]
[null,1,12,14,-6,null,null,null,null,69,377,60,67]
[null,-22,3,5,4,null,null,null,null,-176,60,534,-156]
[null,11,6,4,12,null,null,null,null,255,67,-156,317]
[]
["MATRICE DE CHOLESKY DE LA MATRICE SUIVANTE"]
[]
[]
[null,{"$f":"J7:M10","v":219},69,-176,255,null,null,null,null,{"$f":"cholesky(B15:E18)","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,69,377,60,67,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,-176,60,534,-156,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,255,67,-156,317,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[]
["VERIFICATION PAR LE CALCUL DU CARRE DE LA MATRICE DE CHOLESKY: A . TA"]
[]
[null,{"$f":"J15:M18","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,null,null,{"$f":"MMULT(B22:E25,TRANSPOSE(B22:E25))","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[]
["DETERMINANT DE LA MATRICE INITIALE"]
[]
[null,{"$f":"+J7:M10","v":219},69,-176,255,null,null,null,null,{"$f":"MDETERM(B29:E32)","v":320123664.00000012}]
[null,69,377,60,67]
[null,-176,60,534,-156]
[null,255,67,-156,317]
[]
["DETERMINANT DE LA MATRICE DE CHOLESKY ET SON CARRE"]
[]
[null,{"$f":"+J15:M18","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,null,null,{"$f":"MDETERM(B36:E39)","v":{"$error":"#NAME?"}}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},null,null,"CARRE",null,{"$f":"J36*J36","v":{"$error":"#NAME?"}}]
[null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[]
["VECTEURS PROPRES et VALEURS PROPRES D'UNE MATRICE"]
[null,null,null,null,null,null,null,null,null,"Valeurs Propres"]
[null,{"$f":"B15:E18","v":219},69,-176,255,null,null,null,null,{"$f":"Valp(B43:E46)","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,69,377,60,67]
[null,-176,60,534,-156,null,null,null,null,"Vecteurs Propres, matrice de passage P"]
[null,255,67,-156,317,null,null,null,null,{"$f":"Vecp(B43:E46)","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[]
["VERIFICATION"]
[]
[null,"PRODUIT DES VALEURS PROPRES",null,null,null,null,null,null,null,{"$f":"PRODUCT(J43:M43)","v":{"$error":"#NAME?"}}]
[]
[null,"DETERMINANT DE LA MATRICE DE PASSAGE",null,null,null,null,null,null,null,{"$f":"MDETERM(J46:M49)","v":{"$error":"#NAME?"}}]
[]
[null,"NORME DES VECTEURS PROPRES",null,null,null,null,null,null,null,{"$f":"SUMSQ(J46:J49)","v":{"$error":"#NAME?"}},{"$f":"SUMSQ(K46:K49)","v":{"$error":"#NAME?"}},{"$f":"SUMSQ(L46:L49)","v":{"$error":"#NAME?"}},{"$f":"SUMSQ(M46:M49)","v":{"$error":"#NAME?"}}]
[null,"Utilisez la fonction SOMME.CARRES"]
[]
[null,"Produit de la matrice par le premier vecteur propre",null,null,null,null,null,null,null,{"$f":"MMULT(B43:E46,J46:J49)","v":{"$error":"#NAME?"}}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[]
[null,"Division de ce produit par le vecteur propre lui même",null,null,null,null,null,null,null,{"$f":"J60:J63/J46:J49","v":{"$error":"#NAME?"}}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"}]
[]
["COMPLEMENT: SECONDE MANIERE D'OBTENIR UNE MATRICE RACINE CARRE"]
[]
[null,"Obtenir la matrice diagonale des valeurs propres",null,null,null,null,null,null,null,"Matrice Diagonale: D"]
[null,null,null,null,null,null,null,null,null,{"$f":"J43","v":{"$error":"#NAME?"}},0,0,0]
[null,null,null,null,null,null,null,null,null,0,{"$f":"K43","v":{"$error":"#NAME?"}},0,0]
[null,null,null,null,null,null,null,null,null,0,0,{"$f":"L43","v":{"$error":"#NAME?"}},0]
[null,null,null,null,null,null,null,null,null,0,0,0,{"$f":"M43","v":{"$error":"#NAME?"}}]
[]
[null,"Prendre les racines carrés des éléments diagonaux",null,null,null,null,null,null,null,{"$f":"SQRT(J73)","v":{"$error":"#NAME?"}},0,0,0]
[null,null,null,null,null,null,null,null,null,0,{"$f":"SQRT(K74)","v":{"$error":"#NAME?"}},0,0]
[null,null,null,null,null,null,null,null,null,0,0,{"$f":"SQRT(L75)","v":{"$error":"#NAME?"}},0]
[null,null,null,null,null,null,null,null,null,0,0,0,{"$f":"SQRT(M76)","v":{"$error":"#NAME?"}}]
[]
[null,"Calculer  P D P-1 , on obtient une matrice racine carrée",null,null,null,null,null,null,null,{"$f":"MMULT((J46:M49),MMULT(J78:M81,MINVERSE(J46:M49)))","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[]
[null,"Vérification",null,null,null,null,null,null,null,{"$f":"MMULT(J83:M86,TRANSPOSE(J83:M86))","v":{"$error":"#NAME?"}},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]
[null,null,null,null,null,null,null,null,null,{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"},{"$error":"#NAME?"}]

{"sheet":"NBHALTON","index":7,"n_rows":17,"n_cols":10,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["FONCTION HALTON"]
["NOMBRES DE HALTON"]
[]
[null,"p","k","Halton","Fraction",null,"p","k ","Halton","Fraction"]
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[null,3,{"$f":"C5+1","v":2},{"$f":"halton(B6,C6)","v":0.66666666666666663},{"$f":"D6","v":0.66666666666666663},null,5,{"$f":"H5+1","v":2},{"$f":"halton(G6,H6)","v":0.4},{"$f":"I6","v":0.4}]
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