(a) Let A and B be square matrices that are unitarily equivalent. Prove that ||A||= ||B||.(b) Let T be a linear operator on a finite-dimensional inner product space V. Define Prove that ||T||= || [T]β||, where β is any orthonormal basis for V.(c) Let V be an infinite-dimensional inner product space with an orthonormal basis {v1, v2, . . .}. Let T be the linear operator on V such that T(vk) = kvk. Prove that ||T|| (defined in (b)) does not exist.

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Asked Dec 31, 2019
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(a) Let A and B be square matrices that are unitarily equivalent. Prove that ||A||= ||B||.

(b) Let T be a linear operator on a finite-dimensional inner product space V. Define Prove that ||T||= || [T]β||, where β is any orthonormal basis for V.

(c) Let V be an infinite-dimensional inner product space with an orthonormal basis {v1, v2, . . .}. Let T be the linear operator on V such that T(vk) = kvk. Prove that ||T|| (defined in (b)) does not exist.

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Given A and B  is unitary equivalent square matrices.

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Let

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