# Accession Number:

## AD0261914

# Title:

## MAHLER MATRICES AND THE EQUATION QA = AQM

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1961-06-01

# Pagination or Media Count:

## 1.0

# Abstract:

Several sets of matrices are defined each set forms an abelian group. The elements of the matrices are 0, 1, -1 and other roots of unity or sums of roots of unity. The determinant, characteristic roots, vectors, and elementary divisors are also found. Thus the matrices form a convenient set of test matrices for a routine which purports to solve a matrix. A typical test matrix may involve nonreal elements if each element of the matrix is replaced by a 2 by 2 matrix in the usual way the roots of the expanded real matrix are the roots of the test matrix and their conjugates. The vectors of the expanded matrix are easily found also. Author