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Theorem 12. Let V be a finite dimensional inner product space and te Hom (V, V). Then linear transformation t is orthogonal if and only if the matrix A of t with respect to an orthonor- mal basis satisfies the condition A'A = I and AA" = 1. %3D

Theorem 12. Let V be a finite dimensional inner product space and te Hom (V, V). Then linear transformation t is orthogonal if and only if the matrix A of t with respect to an orthonor- mal basis satisfies the condition A'A = I and AA" = 1. %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 54EQ
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Theorem 12. Let V be a finite dimensional inner product space and te Hom (V, V). Then linear transformation t is orthogonal if and only if the matrix A of t with respect to an orthonor- mal basis satisfies the condition A'A = I and AA" = 1. %3D
Transcribed Image Text:Theorem 12. Let V be a finite dimensional inner product space and te Hom (V, V). Then linear transformation t is orthogonal if and only if the matrix A of t with respect to an orthonor- mal basis satisfies the condition A'A = I and AA" = 1. %3D
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