- #1
WMDhamnekar
MHB
- 379
- 28
I don't understand the following definition. If we let $u=\langle u,v \rangle$ , $p=\langle p,q\rangle,$ $x=\langle x,y \rangle$,then (x,y)=T(u,v) is given in vector notation by
x=T(u). A coordinate transformation T(u) is differentiable at a point p , if there exists a matrix J(p) for which $\lim_{u\to p}\frac {||T(u)-T(p)-J(p)(u-p)||}{||u-p||}=0.$when it exists, J(p) is the total derivative of T(u). What does this symbol || || indicate?
x=T(u). A coordinate transformation T(u) is differentiable at a point p , if there exists a matrix J(p) for which $\lim_{u\to p}\frac {||T(u)-T(p)-J(p)(u-p)||}{||u-p||}=0.$when it exists, J(p) is the total derivative of T(u). What does this symbol || || indicate?
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