Matrix unit
The set of "m" by "n" matrix units is a basis of the space of "m" by "n" matrices. The product of two matrix units of the same square shape formula_3 satisfies the relation
formula_4
where formula_5 is the Kronecker delta. 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". When multiplied by another matrix, it isolates a specific row or column in arbitrary position. For example, for any 3-by-3 matrix "A":
 formula_6
 formula_7
Properties
For example, the 3 by 3 matrix unit with "i" = 1 and "j" = 2 is
formula_2