Accession Number : AD0620667

Title :   ON STABILIZING MATRICES BY SIMPLE ROW OPERATIONS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Folkman,Jon

Report Date : SEP 1965

Pagination or Media Count : 20

Abstract : If A is a nonsingular matrix, the existence is proved of matrices P and Q, each a product of diagonal and permutation matrices, such that PAQ is stable; i.e., all of its eigenvalues have negative real part. This question arises in attempting to solve the equation Ax = b with an analog computer. The result is an existence theorem rather than an effective algorithm. The problem of finding a computationally practical method of doing what is shown can be done remains open. The effect that the transformation A to PAQ has on the eigenvalues of A in general is investigated. It is shown that for 'almost every' n by n matrix A, given any n complex numbers, there is a diagonal matrix D such that DA has those n numbers as its eigenvalues. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS)), STABILIZATION, PERMUTATIONS, OPERATORS(MATHEMATICS), ANALOG COMPUTERS

Distribution Statement : APPROVED FOR PUBLIC RELEASE