[1 2 3] 9. Let A = |2 2 2. oute was SCourseHoto.com 3 2 1 (a) Explain why A is orthogonally diagonalizable. (b) The vectors V1 = (1,1, 1), v2 = (-1,0,1), and V3 = eigenvalues of A? %3D %3D ectors of A. What are the (c) Find a matrix Q which orthogonally (d) Let P = A. Explain why P is a regular stochastic matri: (e) What is the stationary distribution of P? (f) Consider the graph G with adjacency matrix A, and let m be an even natural number. What is the number of walks of length m between vertices 2 and 3?
[1 2 3] 9. Let A = |2 2 2. oute was SCourseHoto.com 3 2 1 (a) Explain why A is orthogonally diagonalizable. (b) The vectors V1 = (1,1, 1), v2 = (-1,0,1), and V3 = eigenvalues of A? %3D %3D ectors of A. What are the (c) Find a matrix Q which orthogonally (d) Let P = A. Explain why P is a regular stochastic matri: (e) What is the stationary distribution of P? (f) Consider the graph G with adjacency matrix A, and let m be an even natural number. What is the number of walks of length m between vertices 2 and 3?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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