
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 : CARNEGIEMELLON 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 rankreducing number of (A  lambda I). It is shown how the rankreducing 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 rankreducing 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