DLA Terminology and notation

Section 19.2 Terminology and notation

finite-dimensional vector space: a vector space for which there exists a finite spanning set
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infinite-dimensional vector space: a vector space for which there does not exists a finite spanning set
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dimension of a finite-dimensional vector space: the number of vectors required in a basis for the space
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$\dim V$: notation for the dimension of a finite-dimensional vector space $V$
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In the case of an infinite-dimensional space

V,

we might write

\dim V = \infty

to indicate this property. Similarly, we might write

\dim V < \infty

to mean that a space

V

is finite-dimensional.