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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.