Definition: Diagonalisable Matrix

A Square Matrix is diagonalisable if it is similar to a Diagonal Matrix .

Theorem: Eigendecomposition

A Square Matrix is diagonalisable if and only if it has linearly independent eigenvectors .

In that case, can be written as a Matrix Product

where the -th column of is the and is the Diagonal Matrix whose -th diagonal entry is the Eigenvalue to which belongs.

Definition: Eigendecomposition

The eigendecomposition of is the product .