Identity matrix

In matrix algebra, the identity matrix is a square matrix which has all the entries on the main diagonal equal to one and all the other, off-diagonal, entries equal to zero. The identity matrix acts as the identity element for matrix multiplication. Its entries are those of the Kronecker delta. The identity matrix represents the identity function as a linear operator on a vector space.

The identity matrix is also known as unit matrix because it possesses many of the properties of the multiplicative unit of an algebraic field.

\mathbf{E}\; \stackrel{\mathrm{def}}{=}\; \begin{pmatrix} 1    & 0    & 0 & \cdots & 0      & 0 \\ 0    & 1    & 0 &        & \cdots & 0 \\ 0    & 0    & 1 &        & \cdots & 0 \\ \vdots&     &   & \ddots &        &\vdots \\ \cdots&\cdots&  &        & 1      & 0 \\ 0    & 0    & 0 & \cdots & 0      & 1 \\ \end{pmatrix} $$ The identity matrix is often indicated by E from the German Einheitsmatrix (unit matrix); I (from identity) is used as well.