I am looking for an elegant proof of the following: Let $A,B \in \mathbb{K}^{n \times n}$ be diagonalizable matrices, and $P_A, P_B$ their characteristic polynomials. Then:
$A, B$ similar $\Leftrightarrow$ $P_A = P_B$
I am somehow stuck at this.
I am looking for an elegant proof of the following: Let $A,B \in \mathbb{K}^{n \times n}$ be diagonalizable matrices, and $P_A, P_B$ their characteristic polynomials. Then:
$A, B$ similar $\Leftrightarrow$ $P_A = P_B$
I am somehow stuck at this.