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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.

MSC:
15A42 Inequalities involving eigenvalues and eigenvectors
15A18 Eigenvalues, singular values, and eigenvectors
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[1] Horn, R.A.; Johnson, C.R., Topics in matrix analysis, (1991), 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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