IEVref: 102-06-22 ID: Language: en Status: Standard Term: norm of a matrix Synonym1: Synonym2: Synonym3: Symbol: Definition: for a square matrix A of order n with the real or complex elements Aij, non-negative number $‖A‖=\sqrt{\mathrm{tr}\left(A{A}^{H}\right)}=\sqrt{\sum _{i,j=1}^{n}{|{A}_{ij}|}^{2}}$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 Source: Replaces: 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 CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: