Let A be a symmetric n x n matrix. a) Show that if u, ER", then (Au) vu (Av). b) Show that if A has distinct eigenvalues A₁ and A2, with corresponding eigenvectors v₁ and v2, then v₁ and 2 are orthogonal.
Let A be a symmetric n x n matrix. a) Show that if u, ER", then (Au) vu (Av). b) Show that if A has distinct eigenvalues A₁ and A2, with corresponding eigenvectors v₁ and v2, then v₁ and 2 are orthogonal.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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