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IEVref:102-06-28ID:
Language:enStatus: Standard
Term: unitary matrix
Synonym1:
Synonym2:
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Symbol:
Definition: 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.


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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