Question

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.

Step 1

We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered

Step 2

Given *A* and *B * is unitary equivalent square matrices.

Step 3

Let

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