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We now see that the problem we studied in Section 7.2, that of diagonalizing a matrix A, may be viewed as the problem of
finding a diagonal matrix D that is similar to A, or as the problem of finding a basis with respect to which the linear
transformation defined by A is diagonal.
Exercise Set 8.5
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In Exercises 1–7 find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect
to the basis .
is defined by
1.
and , where
is defined by
2.
and , where
is the rotation about the origin through 45°; B and are the bases in Exercise 1.
3.
is defined by
4.
B is the standard basis for and , where
