Similarity of Matrix
·
Mathematics/Linear Algebra
Similar Definition 1. Let $A, B \in M_{n \times n}(F)$. We say that $B$ is similar to $A$ if $\exists Q \in M_{n \times n}$ such that $Q$ is invertible and $B = Q^{-1}AQ$. Property Property. Let $A, B \in M_{n \times n}(F)$ be the similar matrices. Then (a) $A$ and $B$ have the same characteristic polynomial. Proof. (a) Since $A$ and $B$ are similar, $\exists$ invertible $Q \in M_{n \times n}(F)..