# 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 $\mathbb{R}$, $$R(x) = \frac{x^T A x}{x^Tx}$$ […]