- Recall that if the matrix A is square (real or complex) then a diagonalisation may exist.
- This is clearly very useful for easy calculation of many important problems as we saw last week.
- If a diagonalisation doesn't exist, then there is always a triangularisation via Schur Decomposition.

- But non-square matrices donâ€™t have eigenvalues, so what can we do?
- You are about to learn the most useful diagonal decomposition that works for all matrices: Singular Value Decomposition.