# Definition A *diagonalizable* (or non-defective) [[Matrix]] is one similar to a diagonal matrix, i.e., $ A \in F^{n \times n} \text{ diagonalizable } \iff \exists\, P, P^{-1} \in F^{n \times n} : P^{-1} A P \text{ diagonal } $ where $F$ is the [[field]] from which the components of $A$ are taken and $n$ is $As [[dimension]].