Editing Zero matrix (section)

{{Short description|Matrix whose entries are all 0}}
In [[mathematics]], particularly [[linear algebra]], a '''zero matrix''' or '''null matrix''' is a [[matrix (mathematics)|matrix]] all of whose entries are [[0 (number)|zero]]. It also serves as the [[additive identity]] of the [[additive group]] of <math>m \times n</math> matrices, and is denoted by the symbol <math>O</math> or <math>0</math> followed by subscripts corresponding to the dimension of the matrix as the context sees fit.<ref>{{citation|title=Linear Algebra|series=[[Undergraduate Texts in Mathematics]]|first=Serge|last=Lang|authorlink=Serge Lang|publisher=Springer|year=1987|isbn=9780387964126|page=25|url=https://books.google.com/books?id=0DUXym7QWfYC&pg=PA25|quotation=We have a zero matrix in which ''a<sub>ij</sub>''&nbsp;=&nbsp;0 for all ''i'',&nbsp;''j''. ... We shall write it&nbsp;''O''.}}</ref><ref>{{Cite web|title=Intro to zero matrices (article) {{!}} Matrices|url=https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-addition-and-scalar-multiplication/a/intro-to-zero-matrices|access-date=2020-08-13|website=Khan Academy|language=en}}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Zero Matrix|url=https://mathworld.wolfram.com/ZeroMatrix.html|access-date=2020-08-13|website=mathworld.wolfram.com|language=en}}</ref> Some examples of zero matrices are

:<math>
0_{1,1} = \begin{bmatrix}
0 \end{bmatrix}
,\ 
0_{2,2} = \begin{bmatrix}
0 & 0 \\
0 & 0 \end{bmatrix}
,\ 
0_{2,3} = \begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \end{bmatrix}
.\ 
</math>