Helmke, Uwe; Shayman, Mark A. Critical points of matrix least squares distance functions. (English) Zbl 0816.15026 Linear Algebra Appl. 215, 1-19 (1995). The authors determine the critical points and the local minimum of the Frobenius distance function \(\| A - X \|^ 2\) on varieties of fixed rank symmetric, skew-symmetric, and rectangular matrices \(X\). Reviewer: J.Zemánek (Warszawa) Cited in 15 Documents MSC: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory Keywords:critical points; local minimum; Frobenius distance function; rectangular matrices PDF BibTeX XML Cite \textit{U. Helmke} and \textit{M. A. Shayman}, Linear Algebra Appl. 215, 1--19 (1995; Zbl 0816.15026) Full Text: DOI References: [1] Eckart, G.; Young, G., The approximation of one matrix by another of lower rank, Psychometrika, 1, 211-218, (1936) · JFM 62.1075.02 [2] Golub, G.H.; Van Loan, C., An analysis of the total least squares problem, SIAM J. numer. anal., 17, 883, (1980) · Zbl 0468.65011 [3] Golub, G.H.; Hoffmann, A.; Stewart, G.W., A generalization of the Eckart-Young-mirsky matrix approximation theorem, Linear algebra appl., 88/89, 317-327, (1987) · Zbl 0623.15020 [4] Higham, N.J., Computing a nearest symmetric positive semidefinite matrix, Linear algebra appl., 103, 103-118, (1988) · Zbl 0649.65026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.