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[parent] stationary point (Definition)

Suppose $ V$ is a vector space and $ L\colon V\to \mathbbmss{R}$ is a map. Then $ v\in V$ is a stationary point of $ L$ provided that

$\displaystyle \frac{d}{dt}L(v+t u)\Big\vert _{t=0} =0 $
for all $ u\in V$. In this case $ u$ is called a variation of $ v$.



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Cross-references: variation, point, map, vector space
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This is version 2 of stationary point, born on 2005-10-29, modified 2006-02-04.
Object id is 7457, canonical name is StationaryPoint.
Accessed 1546 times total.

Classification:
AMS MSC: 47A60 (Operator theory :: General theory of linear operators :: Functional calculus)
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