Partitions of a vector space
Copyright policy )Partitions of a vector space
Partitions of groups have been studied by several authors. J.W. Young proved in [6] that if an abelian group has a non-trivial partition, the group must be an elementary abelian p-group. Since such a group can be represented as the additive group of some V,,(p) -and U is a subgroup of V,(p) iff U is a subspace of V,(p) partitions of V,(q) is a generalization of partitions of abelian groups. Herzog and Schonheim [2] proved that if V,(q) = Cf v and W = vlxv,x*’ l x Vkr then the kernel K of the linear transformation T: W + V,,(q) defined by
vector space over finite field GF(q), Vector spaces, linear dependence, rank, lineability, partitions, Discrete Mathematics and Combinatorics, Theoretical Computer Science
vector space over finite field GF(q), Vector spaces, linear dependence, rank, lineability, partitions, Discrete Mathematics and Combinatorics, Theoretical Computer Science
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