- #1

- 73

- 0

## 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.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Fairy111
- Start date

- #1

- 73

- 0

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.

- #2

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

Consider the identity matrix...

- #3

- 73

- 0

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?

- #4

- 116

- 0

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

Share: