If U is an n xn orthogonal matrix, prove that the corresponding linear transformation Ty : R" → R" given by Tu(v) = Uv is an isometry.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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If U is an n x n orthogonal matrix, prove that the corresponding linear
transformation Tu : R" → R" given by Tu(v) = Uv is an isometry.
Transcribed Image Text:If U is an n x n orthogonal matrix, prove that the corresponding linear transformation Tu : R" → R" given by Tu(v) = Uv is an isometry.
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