User:IssaRice/Linear algebra/Classification of operators

Let $V$ be a finite-dimensional inner product space, and let $T:V\to V$ be a linear transformation.

Operator name	Description in terms of eigenvectors	Description in terms of diagonalizability
$T$ is diagonalizable
$T$ is normal
$T$ self-adjoint ($T$ is Hermitian)
$T$ is an isometry
$T$ is positive