3. (a) Suppose B {b₁,,bn} is an eigenbasis for T with the corresponding eigenvalues A1,,An. Write down [T] B. = (b) Suppose the matrix if T with respect to some basis A is diagonal. What can we say about the vectors in A? (c) Prove: T is diagonalizable if and only if for any basis A of V, [T]A is similar to a diagonal matrix. (d) Are maps given in problem 1 diagonalizable?

3. (a) Suppose B {b₁,,bn} is an eigenbasis for T with the corresponding eigenvalues A1,,An. Write down [T] B. = (b) Suppose the matrix if T with respect to some basis A is diagonal. What can we say about the vectors in A? (c) Prove: T is diagonalizable if and only if for any basis A of V, [T]A is similar to a diagonal matrix. (d) Are maps given in problem 1 diagonalizable?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 10AEXP

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