Consider the linear transformation T : Mnn Mnn defined by T (X) = XT. Find its

Chapter 6, Problem 12

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QUESTION:

Consider the linear transformation T : Mnn Mnn defined by T (X) = XT. Find its eigenvalues and the corresponding eigenspaces. (Hint: Consider the equationXT = X.)

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QUESTION:

Consider the linear transformation T : Mnn Mnn defined by T (X) = XT. Find its eigenvalues and the corresponding eigenspaces. (Hint: Consider the equationXT = X.)

ANSWER:

Problem 12

Consider the linear transformation  defined by  . Find its eigenvalues and corresponding eigenspaces.

                                                        Step by Step Solution

Step 1 of 2

Given linear transformation is  defined by .

Let  be an eigenvalue of this linear transformation. Then,

 

Hence, eigenvalues of the given linear transformation is 1 or -1.

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