## 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

### Keywords:

lower bound; smallest singular value
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### References:

 [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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