Definition:Dimension of Vector Space/Definition 2

Definition

Let $K$ be a division ring.

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

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

Also see

• Equivalence of Definitions of Dimension of Vector Space

• Results about dimension of a vector space can be found here.

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 4$. Vector Spaces
• 1974: Robert Gilmore: Lie Groups, Lie Algebras and Some of their Applications ... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $4$. LINEAR VECTOR SPACE