Some simple estimation theorems for singular values of a rectangular matrix A are given. They only use the elements of A itself, and in some cases they yield better results than does the Gerschgorin theorem applied to A*A. A bound for the condition number of A may be obtained from them. When A is square, a bound is derived which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude. Their application to perturbation theory of singular values is also discussed.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics