# stationary point

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

 $\frac{d}{dt}L(v+tu)\Big{|}_{t=0}=0$

for all $u\in V$. In this case $u$ is called a variation of $v$.

Title stationary point StationaryPoint 2013-03-22 15:33:21 2013-03-22 15:33:21 matte (1858) matte (1858) 5 matte (1858) Definition msc 47A60