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} […]