Talk:Vector-valued function

Alternate Representations?

The article for Inverse function theorem uses this function in an example:

$F(x,y)={\begin{bmatrix}{e^{x}\cos y}\\{e^{x}\sin y}\\\end{bmatrix}}$

This current article (Vector-valued function) uses this notation:

$\mathbf {r} (t)=f(t)\mathbf {\hat {i}} +g(t)\mathbf {\hat {j}}$

The Inverse function theorem and Jacobian articles seem to be using a kind of shorthand.

If they are accurate, it could be helpful in deciphering the column-vector notation to have something like the following in this current article:

$\mathbf {r} (t)=f(t)\mathbf {\hat {i}} +g(t)\mathbf {\hat {j}} ={\begin{bmatrix}{f(t)}\\{g(t)}\\\end{bmatrix}}$

$\mathbf {r} (x,y)=f(x,y)\mathbf {\hat {i}} +g(x,y)\mathbf {\hat {j}} ={\begin{bmatrix}{f(x,y)}\\{g(x,y)}\\\end{bmatrix}}$

Ac44ck 17:28, 18 May 2007 (UTC)