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Subspace is a mental and physical response to the high levels of endorphins produced during play. Described as similar to a runner’s high this is a good feeling and one to be enjoyed if you ever get there. Items in the series. Subspace Let be a real vector space (e.g., the real continuous functions on a closed interval, two-dimensional Euclidean space, the twice differentiable real functions on, etc.). Then is a real subspace of if is a subset of and, for every, and (the reals ),.
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Let be a realvector space (e.g., the real continuous functions on a closed interval , two-dimensional Euclidean space , the twice differentiable real functions on , etc.). Then is a real subspace of if is a subset of and, for every , and (the reals), and . Let be a homogeneous system of linear equations in , ..., . Then the subset of which consists of all solutions of the system is a subspace of .
More generally, let be a field with , where is prime, and let denote the -dimensional vector space over . The number of -D linear subspaces of is
where this is the q-binomial coefficient(Aigner 1979, Exton 1983). The asymptotic limit is
where
(3) |
(5) |
(Finch 2003), where is a Jacobi theta function and is a q-Pochhammer symbol. The case gives the q-analog of the Wallis formula.
SEE ALSO:q-Binomial Coefficient,Subfield, SubmanifoldREFERENCES:Aigner, M. CombinatorialTheory. New York: Springer-Verlag, 1979.
Exton, H. q-HypergeometricFunctions and Applications. New York: Halstead Press, 1983.
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Finch, S. R. 'Lengyel's Constant.' Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 316-321, 2003.
Referenced on Wolfram|Alpha: SubspaceCITE THIS AS:Weisstein, Eric W. 'Subspace.' From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Subspace.html
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