Category:Definitions/Dimension of Vector Space

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This category contains definitions related to Dimension of Vector Space.
Related results can be found in Category:Dimension of Vector Space.

Let $K$ be a division ring.

Let $V$ be a vector space over $K$.

Definition 1

The dimension of $V$ is the number of vectors in a basis for $V$.

Definition 2

The dimension of $V$ is the maximum cardinality of a linearly independent subset of $V$.