Talk:Jacobian matrix

Would the author of this page please note that in TeX, "sin" and "cos" should be preceded by backslashes so that they will not be set in italics, and the proper amount of space between "f(x)" and "dx" is achieved by a backslash followed by a comma. So write this:
 * $$\int\sin x\,dx$$

and not this:
 * $$\int sin x dx.$$

Michael Hardy 20:23 Mar 26, 2003 (UTC)

I was horrified by some of the content of this page, and have corrected it. The first sentence said it's about differential equations; that is complete nonsense. A vector-valued differentiable function of a vector variable is not a "system of differential equations"! The article also said "spaces" when what was meant was individual points in a space. Michael Hardy 20:32 Mar 26, 2003 (UTC)


 * the Jacobian matrix is the matrix of all first-order partial derivatives of scalar components of a vector-valued function F of a vector variable, with respect to the scalar-valued components of the argument to F

The above sentence is terrible. I have a maths degree and it took me about 4 reads to understand it. WE need an opener which gives a general idea of what a Jacobian is, and then a clearer version of the above -- Tarquin 21:40 Mar 26, 2003 (UTC) - i agree, it is very unclear. and i don't think it's even mathematically correct. why do they say 'vector variable', when they are refering to a 'vector'? frankly, this sounds intentionally unclear. i'll restrain myself, out of civility, from quoting Nietzsche regarding those who seek to be understood vs. those who seek the to be incomprehensible. I am returning it to how it was before the change, and people can modify it from there.

Kevin Baas 2003.03.26

also, i'd like to clear up that spaces, surfaces, and curves are not explicitly defined except in 3 dimensional cartesian space, which would amount to a system of 3 variables. They are used as conceptual tools to help elicit a visual comprehension of the proof in which they are used. They do retain, however, their usuall relations, space>surface>curve>0. a curve can be anywhere from 1 dimensional to N-2 dimensional, where N is the manifold under analysis. A surface can be anywhere from 2 to N-1, and a surface of N-1 dimensions is called a hyper-surface. A point, however, by definition is zero-dimensional, i.e. it is a scalar, and being such, has no derivatives, and has nothing to do with Jacobians.

I have reinserted the text that you have removed, that a reader might from it get a good _understanding_ of what a jacobian is. Please don't make this become an issue.

Kevin Baas 2003.03.26

It still doesn't tell a non-mathematician what it is for, why it is interesting, etc. And please don't remove context links! -- Tarquin 22:19 Mar 26, 2003 (UTC)

sorry about that. i didn't mean to. i was copying and pasting from an earlier version. i'll be more carefull next time. thanks. i don't pretend to be explaining why it is interesting, and am not sure how well you can explain to a non-mathematian what a jacobian is. i agree that these should, ideally, both be in an intro, but i have no idea how to write it. again, sorry about the context link.

Kevin Baas 2003.03.26

What's the consensus here on combining jacobian and jacobian matrix to one page, wherein the jacobian is refered to as the jacobian determinant (as it is commonly done in practice)

Kevin Baas 2003.03.26


 * I think that's a good idea, since "Jacobian" is sometimes used for the matrix and sometimes for the determinant. I'll merge everything under Jacobian and keep the two terms separate. AxelBoldt 16:26 May 3, 2003 (UTC)