Finite Vector Spaces
Apart from the trivial case of a zero-dimensional space over any field, a vector space over a field F has a finite number of elements if and only if F is a finite field and the vector space has a finite dimension. Thus we have Fq, the unique finite field (up to isomorphism, of course) with q elements. Here q must be a power of a prime (q = pm with p prime). Then any n-dimensional vector space V over Fq will have qn elements. Note that the number of elements in V is also the power of a prime. The primary example of such a space is the coordinate space (Fq)n.
Read more about this topic: Examples Of Vector Spaces
Famous quotes containing the words finite and/or spaces:
“The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
—Blaise Pascal (1623–1662)
“We should read history as little critically as we consider the landscape, and be more interested by the atmospheric tints and various lights and shades which the intervening spaces create than by its groundwork and composition.”
—Henry David Thoreau (1817–1862)