Let A be any invertible n x n matrix. Show that for u, v in Rn, the formula (u, v) = (Au)· (Av) = (Au)" (Av) Defines an inner product on Rn.
Let A be any invertible n x n matrix. Show that for u, v in Rn, the formula (u, v) = (Au)· (Av) = (Au)" (Av) Defines an inner product on Rn.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 50EQ
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