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.
PROOF
TODO
Definition: Eigendecomposition
The eigendecomposition of is the product .