For a nondefective matrix A ∈ Cn×n, the known inequalities |λk|/χ \ ̌ σk \ ̌ |λk|χ express a bound on the possible ratio between the kth singular value σk of A and its kth eigenvalue λk, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics