Vector Space of Matrices

Theorem: Vector Space of Matrices

The set $F^{m\times n}$ of all $m\times n$-matrices and the field $F$ form a Vector Space $(F^{m\times n},F,+,\cdot )$ together with the addition and Scalar Multiplication for matrices.

Note: Zero Vector

The zero vector of this Vector Space is the Zero Matrix.

PROOF

TODO