Category:Definitions/Dimension (Linear Algebra)

This category contains definitions related to dimension in the context of linear algebra.
Related results can be found in Category:Dimension (Linear Algebra).

Module

Let $R$ be a ring with unity.

Let $G$ be a unitary $R$-module which has a basis of $n$ elements.

Then $G$ is said to have a dimension of $n$ or to be $n$-dimensional.

Vector Space

Let $K$ be a division ring.

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

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