# Accession Number:

## AD0651258

# Title:

## A SPECTRAL CHARACTERIZATION OF STOCHASTIC MATRICES.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1967-01-01

# Pagination or Media Count:

## 13.0

# Abstract:

Let A be an vector product of n an n matrix over a field F with identity element 1. The matrix A is called row column stochastic if all row column sums of A equal 1. The following characterization is obtained A is row or column stochastic if and only if 1 is a characteristic root of PA for all vector product of n an n permutation matrices P. The problem is then varied and all matrices A are determined for which the spectrum of A is the same as the spectrum of PA for all vector product of n an n permutation matrices P. In case the characteristic of F is either 0 or relatively prime to n, the description is very simple either all row vectors or all column vectors are identical. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability