Accession Number : AD0700922

Title :   REDUCING THE RANK OF (A - LAMBDA B) USING THE ROOTS OF A GENERALIZED CHARACTERISTIC POLYNOMIAL.

Descriptive Note : Research rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

Personal Author(s) : Thompson,Gerald L. ; Weil,Roman L. , Jr

Report Date : JAN 1970

Pagination or Media Count : 14

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.

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), POLYNOMIALS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE