A zero matrix is a matrix \(E\in M_{m\times n}(F)\) of the form
$$ O:=\pmatrix{ 0 & 0 & \ldots & 0 \cr 0 & 0 & \ldots & 0 \cr \vdots & \vdots & \ddots & \vdots \cr 0 & 0 & \ldots & 0 \cr }$$ In \(O\), all elements equal \(0\in F\).
As a special case, a zero vector is a vector of the form
$$o=\pmatrix{0\\\vdots\\0},$$
or transposed,
$$o^T=\pmatrix{0,&\ldots,&0}.$$
Corollaries: 1
Examples: 2 3
Proofs: 4 5
Propositions: 6
