Basis

Definition: Basis

A basis of a Vector Space $(V,K,+,\cdot )$ is a linearly independent spanning set.md) of $(V,K,+,\cdot )$.

Equivalent Definition

A set $B$ of vectors is a Basis of a Vector Space $(V,F,+,\cdot )$ if and only if $B$ is a maximally linearly independent.

PROOF

TODO

Equivalent Definition

A set $B$ of vectors from is a Basis of a Vector Space $(V,F,+,\cdot )$ if and only if $B$ is a minimal spanning set.md).

PROOF

TODO