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Area Mathematics - General concepts and linear algebra / Matrices

IEV ref102-06-28

en
unitary matrix
regular square matrix A with complex elements for which the inverse A−1 is equal to the Hermitian conjugate matrix AH

Note 1 to entry: For a unitary matrix with elements Aij:

i A ij A ik * = δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaGccaWGbbWaa0baaSqaaiaadMga caWGRbaabaGaaiOkaaaaaeaacaWGPbaabeqdcqGHris5aOGaeyypa0 JaeqiTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@436E@ and k A ik A jk * = δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaGccaWGbbWaa0baaSqaaiaadMga caWGRbaabaGaaiOkaaaaaeaacaWGPbaabeqdcqGHris5aOGaeyypa0 JaeqiTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@436E@

where δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiabes7aKnaaBaaale aacaWGQbGaam4Aaaqabaaaaa@3900@ and δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiabes7aKnaaBaaale aacaWGQbGaam4Aaaqabaaaaa@3900@ are Kronecker deltas.

Note 2 to entry: Any orthogonal matrix with real elements is a unitary matrix.


fr
matrice unitaire, f
matrice carrée régulière A à éléments complexes dont l’inverse A−1 est égale à l’adjointe AH

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

i A ij A ik * = δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaGccaWGbbWaa0baaSqaaiaadMga caWGRbaabaGaaiOkaaaaaeaacaWGPbaabeqdcqGHris5aOGaeyypa0 JaeqiTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@436E@ et k A ik A jk * = δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqafabaGaamyqam aaBaaaleaacaWGPbGaamOAaaqabaGccaWGbbWaa0baaSqaaiaadMga caWGRbaabaGaaiOkaaaaaeaacaWGPbaabeqdcqGHris5aOGaeyypa0 JaeqiTdq2aaSbaaSqaaiaadQgacaWGRbaabeaaaaa@436E@

δ jk MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiabes7aKnaaBaaale aacaWGQbGaam4Aaaqabaaaaa@3900@ et δ ij MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiabes7aKnaaBaaale aacaWGQbGaam4Aaaqabaaaaa@3900@ sont des symboles de Kronecker.

Note 2 à l'article: Toute matrice orthogonale à éléments réels est une matrice unitaire.


de
unitäre Matrix, f

es
matriz unitaria

ja
ユニタリー行列

pl
macierz unitarna

pt
matriz unitária

sr
унитарна матрица, ж јд

sv
enhetsmatris

zh
酉矩阵

Publication date: 2008-08
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