Let $n\in\mathbb{N}$, let $M_n(\mathbb{R})$ denote the set of real $n\times n$ matrices, let $I_n\in M_n(\mathbb{R})$ denote the $n\times n$ identity matrix, and let
for every $x,y\in\mathbb{R}^n$, where $\langle\cdot,\cdot\rangle$ denotes the standard Euclidean [inner product](/page/Inner%20Product) on $\mathbb{R}^n$.