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Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.

Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.
Transcribed Image Text:Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.
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