help me
- Subject: [mg3393] help me
- From: ruivo at grupo.bfe.pt (Joaquim Azevedo)
- Date: 3 Mar 1996 09:19:15 -0600
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: daemon at wri.com
I am a mathematical student. In this moment I study graph theory, but I have some problems to answer the question above. I would like some help, because I can not get contact with my teacher, and I have examination in two days. Please answer me. Problem: A non-negative real matrix Q is doubly stochastic if the sum of the entries in each row of Q is 1 and sum of the entries in each column of Q is 1. A Permutation matrix is a (0,1)-matrix which has exactly one 1 in each row and each column. (Thus every permutation matrix is doubly stochastic.) Show that: (a) every doubly stochastic matrix is necessarily square; (b) every doubly stochastic matrix Q can be expressed as convex linear combination of permutation matrices; that is Q = c1P1 + c2P2 + ... + ckPk where each Pi is a permutation matrix, each ci is a non-negative real number, and ( ci = 1 (i=1,...,k)