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Theorem 8. Let B = {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear transformation t from V to an inner-product space V' is orthogonal if and only if the set {t (u), t (u2),..., t (u,)} is orthogonal in V'.

Theorem 8. Let B = {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear transformation t from V to an inner-product space V' is orthogonal if and only if the set {t (u), t (u2),..., t (u,)} is orthogonal in V'.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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Theorem 8. Let B= {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear transformation t from V to an inner-product space V' is orthogonal if and only if the set {t (u), t (u2),..., t (u,)} is orthogonal in V'.
Transcribed Image Text:Theorem 8. Let B= {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear transformation t from V to an inner-product space V' is orthogonal if and only if the set {t (u), t (u2),..., t (u,)} is orthogonal in V'.
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