Abstract
Majorization has been used in two areas in numerical analysis: (i) finding a matrix closest to a given matrix, and (ii) obtaining bounds for the condition number and norm of a matrix. Both (i) and (ii) depend on a relation between unitarily invariant norms and symmetric gauge functions (see 3.I.1) obtained by von Neumann (1937). Majorization arises from the fact that symmetric gauge functions are Schur-convex.KeywordsCondition NumberComplex MatrixRidge RegressionHermitian MatrixUnitary MatriceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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