16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.5.14

Linear Transformations

Mathematics — Linear Algebra · separating-functional-characteristic-zero

Problem

Let FF be a field of characteristic zero and let VV be a finite-dimensional vector space over FF. If α1,…,αm\alpha_1, \ldots, \alpha_m are finitely many vectors in VV, each different from the zero vector, prove that there is a linear functional ff on VV such that f(αi)≠0,i=1,…,m.f(\alpha_i) \neq 0, \quad i = 1, \ldots, m.

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