> [!summary] The identity matrix is a special $m\times n$ matrix whose values on the diagonal are 1 >[!info]+ Read Time **⏱ 1 min** # Definition The identity matrix is a $m \times n$ [[Square Matrix|square matrix]] where the entries on the [[Diagonal Matrix|diagonal]] are 1. Any values off the diagonal are zero. Any matrix times the respective $m\times n$ return the same matrix. Similarly to how $3 \times 1=3$. In general, the identity matrix ($I$) is as follows $ I_n = \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end{bmatrix} $ The identity matrix can also be written using [[Diagonal Matrix|diagonal notation]] as $I = \text{diag}(1,1,\dots, 1)$ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/iks8wCfPerU?si=7fcQDY0-skXPLbsK" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>