REDUCING THE RANK OF (A - LAMBDA B) USING THE ROOTS OF A GENERALIZED CHARACTERISTIC POLYNOMIAL.
Abstract
The rank of the n X n matrix (A - lambda I) is n- J(lambda) when lambda is an eigenvalue occurring in J(lambda) = or > 0 Jordan blocks of the Jordan normal form of A. An analogous expression for the rank of (A - lambda B) is derived for general m X n matrices. When J(lambda) 0, lambda is a rank-reducing number of (A - lambda I). It is shown how the rank-reducing properties of eigenvalues can be extended to m X n matrix expressions (A - lambda B). In particular a constructive way is given for deriving a polynomial P(lambda, A, B) whose roots are the only rank-reducing numbers of (A - lambda B). This polynomial is referred to as the characteristic polynomial of A relative to B.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0700922
Entities
People
- Gerald L. Thompson
- Roman L. Weil Jr.
Organizations
- Carnegie Mellon University