- #1
MikeDietrich
- 31
- 0
Homework Statement
If two 3 x 3 matrices A and B have the eigenvalues 1, 2, and 3, then A must be similar to B. True or False and why.
Homework Equations
A is similar to B iff B = S^-1AS
The Attempt at a Solution
I know that if A and B are similar then they have the same eigenvalues but the same does not always hold true the other way. For example, [1 0 ## 0 1] and [1 1 ## 0 1] both have eigenvalues of 1 and 1 but the first is diagonalizable and the second is not so they are not similar. However, I cannot find a counterexample for a 3 x 3 matrix. Any thoughts? Thank you!