basic_tools:variational_calculus:fundamental_lemma
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basic_tools:variational_calculus:fundamental_lemma [2018/03/10 15:07] iiqof created Moved the Variational Calculus Fundamental Lemma here |
basic_tools:variational_calculus:fundamental_lemma [2018/03/12 15:55] (current) jakobadmin |
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| ** Remark ** | ** Remark ** | ||
| This is analogous to the vector algebra proposition, let $v,w\in V$, where $V$ is a vector space. If $v\cdot w = 0$ for all $w\in V$ then $v=0$. In fact, if you dig deeper, it is the same result: the space of continuous functions from $a$ to $b$ is a vector space, and we can define the integral of the multiplication as the inner product! | This is analogous to the vector algebra proposition, let $v,w\in V$, where $V$ is a vector space. If $v\cdot w = 0$ for all $w\in V$ then $v=0$. In fact, if you dig deeper, it is the same result: the space of continuous functions from $a$ to $b$ is a vector space, and we can define the integral of the multiplication as the inner product! | ||
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| + | __ References __ | ||
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| + | * Calculus of Variations - Gelfand and Fomin. | ||
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basic_tools/variational_calculus/fundamental_lemma.1520690842.txt.gz ยท Last modified: 2018/03/10 14:07 (external edit)
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