Diagonalisation

A diagonal matrix is a matrix that has non-zero entries only on the diagonal.

A matrix is diagonalisable if P^-1AP = D. To diagonalise a matrix is to find P such that the preceding condition is met.

If P^-1AP = D then AP = PD
 * P is made up of the eigenvectors of matrix A
 * D is made up of eigenvalues of A
 * Much easier to check this condition

Eigenvalues, eigenvectors and diagonalisation
 * Eigenvectors corresponding to distinct eigenvalues are linearly independent
 * If an n x n matrix has n distinct eigenvalues, then it is diagonalisable
 * Converse is not true however. There are n x n without n distinct eigenvalues who can be diagonalisable.