A matrix is diagonalisable if is similar to a diagonal matrix. That is, if there exists a such that:
…where is a diagonal matrix. can be found by means of eigenvalues and eigenvectors.
Let with a vector space on with finite dimension.
Then, the following statements are equivalent:
- is diagonalisable
- There exists a basis for such that is diagonalisable
- The matrix is diagonalisable for any basis of
A matrix is diagonalisable if and only if is diagonalisable.