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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,

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

Mentioned in:

Corollaries: 1
Examples: 2 3
Proofs: 4 5
Propositions: 6

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References

Bibliography

1. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994