1. Let A be an n x n matrix. What does it mean for A to be
diagonalizable?
For A to be diagonalizable means that there exists some
diagonal n x n matrix D and some invertible n x n matrix P such
that A = PDP-1.
2. Suppose A is similar to B. What does this mean?
B = P-1AP.
3. Put questions 1 and 2 together by completing the following
sentence ... If A is diagonalizable, then A is similar to a
__________ matrix D, where the entries on the main diagonal of
D are the __________ of A.
diagonal; eigenvalues
4. If A is diagonalizable, how many linearly independent
eigenvectors does A have?
n
5. If A is diagonalizable, say D is the diagonal matrix, what are
the entries on the main diagonal of D?
The eigenvalues of A.