Linear Transformation Question.

mslodyczka

Hi,
I'm having trouble with part two of this question. If anyone can help me out with this I would appreciate it. Thanks,
Mike

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fopc

Some suggetions:

Understand why not all matrices are diagonalizable.

Let's assume this one is and let's call it A (i.e., A is the
representation of linear map T relative to standard basis E).

Let diagonal matrix D represent T relative to basis B.

Task: Find S such that D = S^-1AS. The columns of S are
the members of B. Done.

(Note This is an equivalence relation on matrices.
Matrices A and D are *similar*.
This should give some guidance in answering question iii.)

How to find S?
Write out the characteristic polynomial equation for A.
Solve it. The roots are key. The vectors associated with
these roots will make up the columns of S.