Find out if nxn matrix is diagonalisable based on det(XI-A)

[Fairy111]

Homework Statement

If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.

Homework Equations

The Attempt at a Solution

 

[matt grime]

Consider the identity matrix...

 

[Fairy111]

The identity matrix has only one distinct solution, 1, but it is diagonalisable...

So how do you go about checking whether or not a matrix is diagonalisable or not?

 

[Random Variable]

A nxn square matrix is diagonizable if it has n linearly independent eigenvectors. Having n distinct eigenvalues is sufficient but not necessary for diagonalizability.