A square matrix are said to be diagonalizable if it is similar to a diagonal matrix.
Formally a square matrix is said to be diagonalizable if there exists a diagonal matrix such that for some square matrix
For an matrix to be diagonalizable it must have linearly independent eigenvectors.
In this case for
Where notably is the eigenvector of the associated eigenvalue .
Notably this means that if an has distinct eigenvalues it is automatically diagonalizable, however the converse is not true.