Single-entry matrix

In mathematics a single-entry matrix is a matrix where a single matrix and the rest of the elements are zero,[1][2] e.g.,

\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.:

\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:

\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]

References

  1. ↑ Kaare Brandt Petersen & Michael Syskind Pedersen (2008-02-16). "The Matrix Cookbook".
  2. ↑ 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.
  3. ↑ Examples: