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Reference.org
Zero matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, particularly <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, a zero matrix or null matrix is a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> all of whose entries are <a href="/facts/0_(number)/4NBRtKHc">zero</a>. It also serves as the <a href="/facts/Additive_identity/wNDDkXJe">additive identity</a> of the <a href="/facts/Additive_group/djWVpp9D">additive group</a> of m × n {\displaystyle m\times n} matrices, and is denoted by the symbol O {\displaystyle O} or 0 {\displaystyle 0} followed by subscripts corresponding to the dimension of the matrix as the context sees fit. Some examples of zero matrices are </p> 0 1 , 1 = [ 0 ] , 0 2 , 2 = [ 0 0 0 0 ] , 0 2 , 3 = [ 0 0 0 0 0 0 ] . {\displaystyle 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}}.\ }