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Problem 9. An n x n matrix A is called reducible if there is a permutation matrix P such that В с pT AP = where B and D are square matrices of order at least 1. An n x n matrix A is called irreducible if it is not reducible. Show that the n x n primary permutation matrix (S :)- 0 1 0 0 0 1 ... ... A := 0 0 0 1 0 0 1 ... ... is irreducible.

Problem 9. An n x n matrix A is called reducible if there is a permutation matrix P such that В с pT AP = where B and D are square matrices of order at least 1. An n x n matrix A is called irreducible if it is not reducible. Show that the n x n primary permutation matrix (S :)- 0 1 0 0 0 1 ... ... A := 0 0 0 1 0 0 1 ... ... is irreducible.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 41EQ
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Problem 9. An n x n matrix A is called reducible if there is a permutation matrix P such that -(: ) в с pT AP = where B and D are square matrices of order at least 1. An n x n matrix A is called irreducible if it is not reducible. Show that the n x n primary permutation matrix 0 1 0 0 0 1 ... ... A := 0 0 0 1 0 0 1 ... ... is irreducible.
Transcribed Image Text:Problem 9. An n x n matrix A is called reducible if there is a permutation matrix P such that -(: ) в с pT AP = where B and D are square matrices of order at least 1. An n x n matrix A is called irreducible if it is not reducible. Show that the n x n primary permutation matrix 0 1 0 0 0 1 ... ... A := 0 0 0 1 0 0 1 ... ... is irreducible.
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