2. Suppose f: E" E" is an isometry given by f(v) = Ae for some n x n matrix A, n2 2. a) Show that g: E" + E" defined by g(v) 34AA" (r) + 69v is not an isometry. b) Show that h: E" E" defined by h(v) A (e) is also an isometry. %3D Justification:

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
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2. Suppose f: E" E" is an isometry given by f(v) = Av for some n xn matrix A, n 2 2.
a) Show that g: E" + E" defined by g(v) = 34AA" (r) + 69v is not an isometry.
b) Show that h: E" - E" defined by h(v) A(v) is also an isometry.
Justification:
Transcribed Image Text:2. Suppose f: E" E" is an isometry given by f(v) = Av for some n xn matrix A, n 2 2. a) Show that g: E" + E" defined by g(v) = 34AA" (r) + 69v is not an isometry. b) Show that h: E" - E" defined by h(v) A(v) is also an isometry. Justification:
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