A SPECTRAL CHARACTERIZATION OF STOCHASTIC MATRICES.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD0651258
Entities
People
- Helmut W. Wielandt
- Richard A. Brualdi
Organizations
- University of Wisconsin–Madison