# characterization of basis of finite dimensional vector space

Let $X$ be a linear space and let $\phi_{i}$ be the linear functional, $\phi_{i}\colon X\to\mathbb{R},1\leq i\leq n$, such as $\displaystyle[\phi_{i}(\upsilon)=0,\forall i=1,2,...,n]\rightarrow[\phi(% \upsilon)=0].$ Then there exist $\lambda_{1},\lambda_{2},...,\lambda_{n}\in\mathbb{R}$ such as $\phi=\sum_{i=1}^{n}\lambda_{i}\phi_{i}$.

Title characterization of basis of finite dimensional vector space CharacterizationOfBasisOfFiniteDimensionalVectorSpace 2013-03-22 15:24:28 2013-03-22 15:24:28 georgiosl (7242) georgiosl (7242) 9 georgiosl (7242) Corollary msc 03E20