# characterization of basis of finite dimensional vector space

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

Title | characterization of basis of finite dimensional vector space |
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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 |