Matrix unit

In linear algebra, a matrix unit is a matrix with only one nonzero entry with value 1.^[1][2] The matrix unit with a 1 in the ith row and jth column is denoted as ${\displaystyle E_{ij}}$. For example, the 3 by 3 matrix unit with i = 1 and j = 2 is $${\displaystyle E_{12}={\begin{bmatrix}0&1&0\\0&0&0\\0&0&0\end{bmatrix}}}$$A vector unit is a standard unit vector.

A single-entry matrix generalizes the matrix unit for matrices with only one nonzero entry of any value, not necessarily of value 1.