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IEVref:102-06-26ID:
Language:enStatus: Standard
Term: orthogonal matrix
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Definition: 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.


Publication date:2008-08
Source:
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
2017-08-25: Corrected order of I and sub tags. LMO
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