Accession Number:

AD0620667

Title:

ON STABILIZING MATRICES BY SIMPLE ROW OPERATIONS,

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CALIF

Personal Author(s):

Report Date:

1965-09-01

Pagination or Media Count:

20.0

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

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE