characterization of basis of finite dimensional vector space

Let $X$ be a linear space and let ${\varphi }_i$ be the linear functional, ${\varphi }_i:X\to ℝ,1\le i\le n$, such as $[{\varphi }_i(\upsilon )=0,\forall i=1,2,\mathrm{\dots },n]\to [\varphi (\upsilon )=0].$ Then there exist ${\lambda }_1,{\lambda }_2,\mathrm{\dots },{\lambda }_n\in ℝ$ such as $\varphi ={\sum }_{i=1}^n{\lambda }_i{\varphi }_i$.

Title	characterization of basis of finite dimensional vector space
Canonical name	CharacterizationOfBasisOfFiniteDimensionalVectorSpace
Date of creation	2013-03-22 15:24:28
Last modified on	2013-03-22 15:24:28
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	9
Author	georgiosl (7242)
Entry type	Corollary
Classification	msc 03E20