Section 20.2 Terminology and notation
- finite-dimensional vector space
a vector space for which there exists a finite spanning set
- infinite-dimensional vector space
a vector space for which there does not exists a finite spanning set
- dimension of a finite-dimensional vector space
the number of vectors required in a basis for the space
- \dim V
notation for the dimension of a finite-dimensional vector space V
Remark 20.2.1.
In the case of an infinite-dimensional space V\text{,} we might write \dim V = \infty to indicate this property. Similarly, we might write \dim V \lt \infty to mean that a space V is finite-dimensional.