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(4) _________
(5) _________
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If A and B are similar matrices, say , then Exercise 21 shows that A and B have the
22. same eigenvalues. Suppose that λ is one of the common eigenvalues and x is a corresponding
eigenvector for A. See if you can find an eigenvector of B corresponding to λ, expressed in terms
of λ, x, and P.
Since the standard basis for is so simple, why would one want to represent a linear operator on
23. in another basis?
Characterize the eigenspace of in Example 4.
24.
Prove that the trace is a similarity invariant.
25.
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