Category:Sufficient Conditions for Basis of Finite Dimensional Vector Space

This category contains pages concerning Sufficient Conditions for Basis of Finite Dimensional Vector Space:

Let $K$ be a division ring.

Let $n \ge 0$ be a natural number.

Let $E$ be an $n$-dimensional vector space over $K$.

Let $B \subseteq E$ be a subset such that $\card B = n$.

The following statements are equivalent:

$(1): \quad$ $B$ is a basis of $E$.

$(2): \quad$ $B$ is linearly independent.

$(3): \quad$ $B$ is a generator for $E$.