
Accession Number : AD0694447
Title : THE ROOTS OF MATRIX PENCILS (Ay = Lambda By): EXISTENCE, CALCULATIONS, AND RELATIONS TO GAME THEORY.
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 : 22 AUG 1969
Pagination or Media Count : 32
Abstract : Given m x n matrices A and B, by a solution to the pencil system of A relative to B we mean a triple lambda not equal to 0, x not equal to 9, y not equal to 0, where lambda is (x), x is 1 x m and y is n x 1, such that both x(Alambda B) = 0 and (Alambda B) y = 0. A canonical form is derived from which it is easy to state conditions for existence of such solutions. By further decomposing the canonical form it is shown that ordinary elimination methods and eigenvalue routines may be used to find pencil solutions. Next the relationship between matrix pencils and matrix games is studied. Finally, the relationship between game theory and dual systems of linear homogeneous equations is developed for both the real and complex cases and applied to pencil systems. (Author)
Descriptors : (*GAME THEORY, *MATRICES(MATHEMATICS)), DIFFERENTIAL EQUATIONS, PERMUTATIONS, ECONOMICS, THEOREMS
Subject Categories : Theoretical Mathematics
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE