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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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