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IEVref: | 102-06-22 | ID: | |

Language: | en | Status: Standard | |

Term: | norm of a matrix | ||

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Definition: | for a square matrix of order An with the real or complex elements A, non-negative number _{ij}$\Vert A\Vert =\sqrt{\mathrm{tr}(A{A}^{H})}=\sqrt{{\displaystyle \sum _{i,j=1}^{n}{\left|{A}_{ij}\right|}^{2}}}$ 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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$\Vert A\Vert =\sqrt{\mathrm{tr}(A{A}^{H})}=\sqrt{{\displaystyle \sum _{i,j=1}^{n}{\left|{A}_{ij}\right|}^{2}}}$

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).