# 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,[1][2] e.g.,

$\displaystyle{ \mathbf{J}^{23} = \left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right]. }$

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.:

$\displaystyle{ \mathbf{J}^{23}\mathbf{A} = \left[ \begin{matrix} 0 & 0& 0 \\ a_{31} & a_{32} & a_{33} \\ 0 & 0 & 0 \end{matrix}\right]. }$

Alternatively, a column-selector when multiplied on the right side:

$\displaystyle{ \mathbf{A}\mathbf{J}^{23} = \left[ \begin{matrix} 0 & 0 & a_{12} \\ 0 & 0 & a_{22} \\ 0 & 0 & a_{32} \end{matrix}\right]. }$

The name, single-entry matrix, is not common, but seen in a few works.[3]

A single-entry vector is a scaled standard unit vector.

## References

1. Shohei Shimizu, Patrick O. Hoyer, Aapo Hyvärinen & Antti Kerminen (2006). "A Linear Non-Gaussian Acyclic Model for Causal Discovery". Journal of Machine Learning Research 7: 2003–2030.
2. Examples:
•
• Marcel Blattner (2009). "B-Rank: A top N Recommendation Algorithm". arXiv:0908.2741 [physics.data-an].