Category:Sufficient Conditions for Basis of Finite Dimensional Vector Space
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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 $E$.
Pages in category "Sufficient Conditions for Basis of Finite Dimensional Vector Space"
The following 3 pages are in this category, out of 3 total.