Definition: Zero Matrix, Zero Vector 

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,

$$o^T=\pmatrix{0,&\ldots,&0}.$$

| | | | | created: 2014-11-05 21:55:59 | modified: 2020-11-29 07:46:13 | by: bookofproofs | references: [1038]