Suppose that ß and y are ordered bases for an n-dimensional real [complex] inner product space V. Prove that if Q is an orthogonal [unitary] n x n matrix that changes y-coordinates into B-coordinates, then ß is orthonormal if and only if y is orthonormal.

Suppose that ß and y are ordered bases for an n-dimensional real [complex] inner product space V. Prove that if Q is an orthogonal [unitary] n x n matrix that changes y-coordinates into B-coordinates, then ß is orthonormal if and only if y is orthonormal.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 25E: Let A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal...

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Question

Suppose that ß and y are ordered bases for an n-dimensional real [complex] inner product space V. Prove that if Q is an
orthogonal [unitary] n x n matrix that changes y-coordinates into B-coordinates, then ß is orthonormal if and only if y is
orthonormal.

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