Is a diagonal matrix diagonalizable?

Question

A matrix $A$ is a diagonalizable if there exists a diagonal matrix $D$ such that $A$ is similar to $D$. If $A$ is a diagonal matrix, though, is it diagonalizable? If so, it would seem $D$ would just be $A$. I suppose my real question is if it is even proper to ask if a diagonal matrix is diagonalizable. (I am writing a proof, and I want to be as correct as possible.)

And yes, it makes sense to ask if a diagonal matrix is diagonalisable. It follows straight from the definition =p. Just conjugate by the identity. — LASV, Dec 05 '13 at 07:05

score 7 · Answer 1 · edited Apr 10 '18 at 00:50

7

Of course a diagonal matrix $D$ is diagonalisable:

$$I_n^{-1} D I_n=D$$

edited Apr 10 '18 at 00:50

Rolazaro Azeveires

653

answered Dec 05 '13 at 07:02

LASV

3,108

Is a diagonal matrix diagonalizable?

1 Answers1