Vector Space/Examples/Arrows through Point in 3D Space
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Example of Vector Space
The set $\mathbf V$ of all arrows through a given point in ordinary $3$-dimensional Euclidean space forms a vector space whose scalar field is the set of real numbers $\R$.
Thus $\mathbf V$ is itself a vector space of $3$ dimensions.
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 32$. Definition of a Vector Space: Example $61$
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 34$. Dimension: Example $65$