Single-entry matrix

In mathematics a single-entry matrix is a matrix where a single element is one and the rest of the elements are zero, e.g.,
It is a specific type of a sparse matrix. The single-entry matrix can be regarded a row-selector when it is multiplied on the left side of the matrix, e.g.:
Alternatively, a column-selector when multiplied on the right side:
The name, single-entry matrix, is not common, but seen in a few works.
A single-entry vector is a scaled standard unit vector.