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Area Mathematics - General concepts and linear algebra / Matrices

IEV ref102-06-26

en
orthogonal matrix
square matrix A for which the inverse A−1 is equal to the transpose matrix AT

Note 1 to entry: For an orthogonal matrix with elements Aij:

i A ij A ik = δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaaabaGaamyAaaqab0GaeyyeIuoa kiaadgeadaWgaaWcbaGaamyAaiaadUgaaeqaaOGaeyypa0dcdaGae8 hTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@4642@ and k A ik A jk = δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaam4AaaqabaaabaGaam4Aaaqab0GaeyyeIuoa kiaadgeadaWgaaWcbaGaamOAaiaadUgaaeqaaOGaeyypa0dcdaGae8 hTdq2aaSbaaSqaaiaadMgacaWGQbaabeaaaaa@4644@

where δjk and δij are Kronecker deltas.


fr
matrice orthogonale, f
matrice carrée régulière A dont l’inverse A−1 est égale à la transposée AT

Note 1 à l'article: Pour une matrice orthogonale d'éléments Aij:

i A ij A ik = δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaaabaGaamyAaaqab0GaeyyeIuoa kiaadgeadaWgaaWcbaGaamyAaiaadUgaaeqaaOGaeyypa0dcdaGae8 hTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@4642@ et k A ik A jk = δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaam4AaaqabaaabaGaam4Aaaqab0GaeyyeIuoa kiaadgeadaWgaaWcbaGaamOAaiaadUgaaeqaaOGaeyypa0dcdaGae8 hTdq2aaSbaaSqaaiaadMgacaWGQbaabeaaaaa@4644@

où δjk et δij sont des symboles de Kronecker.


de
orthogonale Matrix, f

es
matriz ortogonal

ja
直交行列

pl
macierz ortogonalna

pt
matriz ortogonal

sr
ортогонална матрица, ж јд

sv
ortogonal matris

zh
正交矩阵

Publication date: 2008-08
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