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IEVref:102-06-22ID:
Language:enStatus: Standard
Term: norm of a matrix
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Definition: for a square matrix A of order n with the real or complex elements Aij, non-negative number

A= tr(A A H ) = i,j=1 n | A ij | 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaafmaabaGaaCyqaa GaayzcSlaawQa7aiabg2da9maakaaabaqcLbuacaGG0bGaaiOCaOGa aiikaiaahgeacaWHbbWaaWbaaSqabeaajugabiaacIeaaaGccaGGPa aaleqaaOGaeyypa0ZaaOaaaeaadaaeWbqaamaaemaabaGaamyqamaa BaaaleaacaWGPbGaamOAaaqabaaakiaawEa7caGLiWoadaahaaWcbe qaaKqzaeGaaGOmaaaaaSqaaiaadMgacaGGSaGaamOAaiabg2da9Kqz aeGaaGymaaWcbaGaamOBaaqdcqGHris5aaWcbeaaaaa@5560@

Note 1 to entry: The described norm is the "Euclidean norm" or the "Hermitian norm" for the real and the complex case, respectively. Several other norms of a matrix can be defined. Any norm of a matrix has properties similar to the properties of the magnitude of a vector (see Note 1 to entry in IEV 102-03-23).


Publication date:2008-08
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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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