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Area Mathematics - General concepts and linear algebra / Matrices

IEV ref102-06-22

en
norm of a matrix
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).


fr
norme d’une matrice, f
pour une matrice carrée A d'ordre n et d'éléments réels ou complexes Aij, nombre non négatif

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 à l'article: La norme décrite est la «norme euclidienne» ou la «norme hermitienne», pour des éléments réels ou complexes, respectivement. Plusieurs autres normes de matrices peuvent être définies. Toute norme de matrice a des propriétés semblables à celles de la norme d'un vecteur (voir la Note 1 à l’article dans IEV 102-03-23).


de
Norm (einer Matrix), f

es
norma de una matriz

ja
行列のノルム

pl
norma macierzy

pt
norma de uma matriz

sr
норма матрице, ж јд

sv
norm av en matris

zh
矩阵的范

Publication date: 2008-08
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