查看“︁单元素矩阵”︁的源代码

在数学中，'''单元素矩阵'''是一个[[矩阵]]，其中只有一个元素为一，其余元素为零，<ref>{{Cite web|url=http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf|title=The Matrix Cookbook|date=2008-02-16|last=Kaare Brandt Petersen|accessdate=2018-10-01|archive-date=2018-09-20|archive-url=https://web.archive.org/web/20180920213115/http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf|dead-url=no}}</ref><ref>{{Cite journal|title=A Linear Non-Gaussian Acyclic Model for Causal Discovery|author=Shohei Shimizu, Patrick O. Hoyer, Aapo Hyvärinen & Antti Kerminen|url=http://www.cs.helsinki.fi/group/neuroinf/lingam/JMLR06.pdf|journal={{tsl|en|Journal of Machine Learning Research||Journal of Machine Learning Research}}|year=2006|volume=7|pages=2003&ndash;2030|access-date=2018-10-01|archive-date=2017-08-13|archive-url=https://web.archive.org/web/20170813033627/https://www.cs.helsinki.fi/group/neuroinf/lingam/JMLR06.pdf|dead-url=no}}</ref>例如：

:<math>\mathbf{J}^{23} = \left[\begin{matrix}
0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right].</math>

它是[[稀疏矩阵]]的特定类型。 当单元素矩阵在矩阵的左侧相乘时，可以将其视为行选择器，例如：
 
: <math>
 \mathbf{J}^{23}\mathbf{A} = \left[ \begin{matrix} 0 & 0& 0 \\ a_{31} & a_{32} & a_{33} \\ 0 & 0 & 0 \end{matrix}\right].
</math>

或者，在右边乘以列选择器：

: <math>
 \mathbf{A}\mathbf{J}^{23} = \left[ \begin{matrix} 0 & 0 & a_{12} \\ 0 & 0 & a_{22} \\ 0 & 0 & a_{32}  \end{matrix}\right].
</math>

单元素矩阵这个名称并不常见，但在一些书籍中可以看到。<ref>例子：

* {{cite web
 | title = Distributed Gain Matrix Optimization in Non-Regenerative MIMO Relay Networks
 | url = http://www.nari.ee.ethz.ch/wireless/pubs/files/asilomar09r.pdf
 | access-date = 2018-10-01
 | archive-date = 2021-03-05
 | archive-url = https://web.archive.org/web/20210305105910/https://www.nari.ee.ethz.ch/wireless/pubs/files/asilomar09r.pdf
 }}
* {{Cite web
 | author = Marcel Blattner
 | title = B-Rank: A top N Recommendation Algorithm
 | url = https://arxiv.org/pdf/0908.2741.pdf
 | access-date = 2018-10-01
 | archive-date = 2019-08-10
 | archive-url = https://web.archive.org/web/20190810160929/https://arxiv.org/pdf/0908.2741.pdf
 }}</ref>

== 参考文献 ==
{{Reflist}}

{{线性代数小作品}}

[[Category:矩阵]]