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].}](../I/m/ebcc2513677b500e631a8e63ea721fec11a5decd.svg)
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]}](../I/m/e21f4a261c98a6565eabb87e34ac6faf8ee89060.svg)
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]}](../I/m/9823cb6c9476e51abb95866a38fac11bc4fe51df.svg)
The name, single-entry matrix, is not common, but seen in a few works.[3]
References
- ↑ Kaare Brandt Petersen & Michael Syskind Pedersen (2008-02-16). "The Matrix Cookbook" (PDF).
- ↑ Shohei Shimizu, Patrick O. Hoyer, Aapo Hyvärinen & Antti Kerminen (2006). "A Linear Non-Gaussian Acyclic Model for Causal Discovery" (PDF). Journal of Machine Learning Research. 7: 2003–2030.
- ↑ Examples:
- "Distributed Gain Matrix Optimization in Non-Regenerative MIMO Relay Networks" (PDF).
- Marcel Blattner. "B-Rank: A top N Recommendation Algorithm" (PDF).
This article is issued from Wikipedia - version of the 7/13/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.