Definition:Dimension of Vector Space/Finite
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Definition
Let $V$ be a vector space which is $n$-dimensional for some $n \in \N_{\ge 0}$.
Then $V$ is finite dimensional.
The dimension of a finite-dimensional $K$-vector space $V$ is denoted $\map {\dim_K} V$, or just $\map \dim V$.
Also known as
Some sources use a hyphen, thus referring to a finite-dimensional vector space.
Also see
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 33$. Definition of a Basis
- 1994: Robert Messer: Linear Algebra: Gateway to Mathematics: $\S 3.4$