Definition:Dimension (Linear Algebra)

Definition

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 cardinality of an arbitrary basis for $V$.

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Also see

• Results about dimension in the context of linear algebra can be found here.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem