# Does diagonalizable imply symmetric?

Scootertaj
In order to prove my PDE system is well-posed, I need to show that if a matrix is diagonalizable and has only real eigenvalues, then it's symmetric.

## Homework Equations

I've found theorems that relate orthogonally diagonalizable and symmetric matrices, but is that sufficient?

## The Attempt at a Solution

See above.

$$\left(\begin{array}{cc} 1 & 2\\ 0 & 3\end{array}\right)$$