Skip to main content
Logo image

Section 19.2 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 19.2.1.

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.