Definition:Basis of Vector Space/Definition 1
Jump to navigation
Jump to search
Definition
Let $R$ be a division ring.
Let $\struct {G, +_G, \circ}_R$ be an vector space over $R$.
A basis of $G$ is a linearly independent subset of $G$ which is a generator for $G$.
Also see
Linguistic Note
The plural of basis is bases.
This is properly pronounced bay-seez, not bay-siz.
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 4$. Vector Spaces
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 33$. Definition of a Basis
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): $\text{A}.2$: Linear algebra and determinants: Definition $\text{A}.6$