A lower bound for the smallest singular value. (English) Zbl 0768.15012

The authors obtain a lower bound for the smallest singular value of a square complex matrix \(A\) in terms of the determinant and the 2-norm of the columns and rows of \(A\). Examples are given to show that this bound works well for certain classes of matrices.


15A42 Inequalities involving eigenvalues and eigenvectors
15A18 Eigenvalues, singular values, and eigenvectors
Full Text: DOI


[1] Horn, R. A.; Johnson, C. R., Topics in Matrix Analysis (1991), Cambridge U.P: Cambridge U.P New York · Zbl 0729.15001
[2] Higham, N. J., A survey of condition number estimation for triangular matrices, SIAM Rev., 29, 575-596 (1987) · Zbl 0635.65049
[3] Johnson, C. R., A Gersgorin-type lower bound for the smallest singular value, Linear Algebra Appl., 112, 1-7 (1989) · Zbl 0723.15013
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