Identity matrix

In mathematics the identity matrix is the matrix which, when multiplying, does not change the size or values of the matrix by which it is multiplied. The identity matrix is usually denoted <math>I</math> or <math>I_n</math>, and the operation of multiplication is described as,

<math>AI=A</math> or <math>IA=A</math>

The identity matrix is an <math>n\times n</math> matrix where the leading diagonal is ones and all other entries are zero. That is, <math>a_{ii} = 1</math>, and <math>a_{ij} = 0</math> whenever <math>i \neq j</math>.

<math>I=\begin{bmatrix}

1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{bmatrix} </math>