# 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