Proving Real Eigenvalues for Symmetric Matrix Multiplication?

[tom08]

Homework Statement

Given a real diagonal matrix D, and a real symmetric matrix A,

Homework Equations

Let C=D*A.

The Attempt at a Solution

How to prove all the eigenvalues of matrix C are real numbers?

 

[Dick]

Now why would you think that's true?

 

[CompuChip]

Also note this thread.