- #1
Bipolarity
- 776
- 2
Similar matrices share certain properties, such as the determinant, trace, eigenvalues, and characteristic polynomial. In fact, all of these properties can be determined from the character polynomial alone.
However, similar matrices also share the same rank. I was wondering if the rank is also encoded in the characteristic polynomial of the matrix.
In other words, if two matrices have the same characteristic polynomial, need their rank be the same?
I'd like to know the answer, so that I can decide whether to prove or to cook up a counterexample.
Thanks!
BiP
However, similar matrices also share the same rank. I was wondering if the rank is also encoded in the characteristic polynomial of the matrix.
In other words, if two matrices have the same characteristic polynomial, need their rank be the same?
I'd like to know the answer, so that I can decide whether to prove or to cook up a counterexample.
Thanks!
BiP