# Questions tagged [jacobian]

In multivariable calculus, the jacobian matrix of a smooth map at a given point is the matrix of its partial derivatives evaluated at this point.

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### Approximation in Levenberg-Marquardt method

In Levenberg-Marquardt method we have a following update rule $$x_{i+1} = x_i - \left( H - \lambda I \right)^{-1}\;\nabla f(x_i)$$ But in this tutorial is the formula implemented like this ...
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### Derive the Jacobian of u and v with respect to x and y

I want to derive the expression for the Jacobian of u and v with respect to x and y with the following considerations : Consider a small differential rectangular element ABCD in the x-y coordinate ...
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### Question on Partial derivatives in inverse function changing from coordinate systems

I would like to ask a question about partial derivatives in the context of Rotations of coordinate systems. Say we have a coordinate system (unprimed) and its rotated version (primed). If the ...
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### The Jacobian and Particular Solutions to an Underdetermined Equation

I was wondering if the factor $\sqrt{(x')^2 + (y')^2}$ in the line integral formula $$\int_a^b\ f(x,\ y)\ \sqrt{(x')^2 + (y')^2}\ dt$$ can also be thought of as a Jacobian determinant, due to the ...
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### How to compute the Jacobian matrix of a multivariate function in a nonstandard matrix?

Given a function $f:R^2\rightarrow R^2$ such that $f(x,y)=(xy, \cos xy)$, I need to compute the Jacobian matrix Df with respect to the basis $\{(1,0), (1,1)\}$. Not confident in my answer though. ...
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### coordinate transformation By means of Jacobi's theorem

In Einstein's "The Meaning of Relativity" as example of invariant it considers the volume https://en.wikisource.org/wiki/The_Meaning_of_Relativity/Lecture_1: $V=\iiint dx_{1}dx_{2}dx_{3}$ By means ...
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### Solve the integral $\int_0^1\int^1_xy^4e^{xy^2}dydx$.
Solve the integral $\int_0^1\int^1_xy^4e^{xy^2}dydx$. I think that variables substituation is neede here. I've substitute $$\\ \left\{\begin{matrix} u=xy^2\\ v=y \end{matrix}\right. \$$ and ...
A transformation T (u, v) is said to be a conformal transformation if its Jacobian matrix preserves angles between tangent vectors. Consider that the vector $\langle 0,1\rangle$ is parallel to the ...