[1][2] The matrix unit with a 1 in the ith row and jth column is denoted as
A single-entry matrix generalizes the matrix unit for matrices with only one nonzero entry of any value, not necessarily of value 1.
The set of m by n matrix units is a basis of the space of m by n matrices.
[2] The product of two matrix units of the same square shape
{\displaystyle E_{ij}E_{kl}=\delta _{jk}E_{il},}
[2] The group of scalar n-by-n matrices over a ring R is the centralizer of the subset of n-by-n matrix units in the set of n-by-n matrices over R.[2] The matrix norm (induced by the same two vector norms) of a matrix unit is equal to 1.
When multiplied by another matrix, it isolates a specific row or column in arbitrary position.
For example, for any 3-by-3 matrix A:[3] This linear algebra-related article is a stub.