real symmetric matrix

[tom08]

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Let C=D*A.


3. 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 (http://www.physicsforums.com/showthread.php?t=364255).