Monthly Archives: January 2016

The Rayleigh Quotient and the Norm Constraint

This post will try to explain why in the optimization of the Rayleigh Quotient one constrains the norm of \(x\) to be \(\|x\| = 1\) Let's start with the definition, given a symmetric matrix, \(A\), the Rayleigh quotient is defined as a function \(R(x)\) from \(\mathbb{R}^{d}_{0}\) to \(\mathbb{R}\), \begin{equation} R(x) = \frac{x^T A x}{x^Tx} \end{equation} […]