# Rayleigh Quotient variant?

If $A$ is a covariance matrix and I want to get

$\max X^TAX$ where each value of $x$ is between -1 and 1.

Is there a closed-form solution for this?

I understand when $X^TX = 1$ this becomes the original Rayleigh quotient problem.

• Is $X$ a random column vector? – Omnomnomnom Jun 28 '14 at 4:33
• @Omnomnomnom: Right, X is an n x 1 vector – user40923 Jun 28 '14 at 4:45