# 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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### Derivative of $\mathrm{L}_2$ norm of function

I would like to find the derivative of the function $g$ with respect to $(\theta, z)$ where $y$ and $w$ are independent of $(\theta, z)$ and $\parallel\cdot\parallel_2$ denotes the $\mathrm{L}_2$ ...
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### Jacobian / product operator of partial derivative to a diagonal matrix,

I m trying go manually calculate the Back propagation through time of a simple RNN following this 'DL algorithms with Python" book : https://books.google.nl/books?id=8DqlDwAAQBAJ&pg=PA39&...
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### Jacobian Matrix of a Non Linear ODE with time delay

I need help with figuring out the Jacobian Matrix of this non linear ODE system with time delay. Can anyone please walk me through the entire process? Thank you very much.
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### Can't understand the proof of the Time-Rescaling theorem.

I was reading the following paper: The time-rescaling theorem and its application to neural spike train data analysis and I have some difficulties understanding the proof of the time-rescaling-theorem....
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### Propagation of uncertainty for nonlinear combinations

I would like to better understand propagation of uncertainties in case of non-linear combinations. I therefore read this article on Wikipedia. I think I got a good understanding of the first part ...
1answer
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### Derivatives with Jacobian Matrix Composition

Let $h: \mathbb{R}^3 \rightarrow \mathbb{R}$ such that $h(x,y,z)=g(x^2-y^2,y^2-z^2)$ and $g: \mathbb{R}^2 \rightarrow \mathbb{R}$ a differentiable function such that $\nabla g(0,0)=(1,2)$. Determine ...
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### Jacobian for this function (numerical on MATLAB)?

I have two vectors $r$ and $m$. Both vectors are $N\times1$. A function is calculated as - $F(1:N) = \phi r + (r^3 + rm^2)$ $F(N+1:2N) = \phi m + (m^3+mr^2)$ I am having trouble calculating the ...
1answer
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### Derivative of a Matrix w.r.t. its Matrix Square, $\frac{\partial \text{vec}X}{\partial\text{vec}(XX')}$

Let $X$ be a nonsingular square matrix. What is $$\frac{\partial \text{vec}X}{\partial\text{vec}(XX')},$$ where the vec operator stacks all columns of a matrix in a single column vector? It is easy ...
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### Prove that this map isn't invertible on all of $\mathbb R^2$.

Let $F(x,y)=(e^x\cos y, e^x\sin y)$, show that $F$ isn't invertible on all of $\mathbb R^2$, although it's locally invertible everywhere. It's obvious that $F$ is locally invertible everywhere, ...
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### What is the Jacobian of a derivative?

Consider the following system - $\phi u + \frac{1}{2}\frac{d^2u}{dt^2} + u^3 = 0$ The task is to find $\phi$ and $u$ that satisfies the above differential equation. This is just a problem given to ...
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### jacobian matrice and differentiability

I am new here and I actually don´t know how to solve this question How can I show that the following functions are differentiable and how can I determine their derivatives as well as the corresponding ...
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### Testing the accuracy of my Jacobian using second order convergence

I am writing a program to do some numerical analysis on a function and it gets a little tricky dealing with the Jacobian. Being new to this field, there is always the question - did I get the Jacobian ...
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### If $L(X)$ is linear then $L'(X)=L(X)$

Let $L:\mathbb R^n\to \mathbb R^m$ be a linear map, Prove that $L'(X)=L(X)$ for all $X\in \mathbb R^n$. This is what I've done so far, let $X\in \mathbb R^n$ then we know that $$DL(X)=L'(X)=J_L(X)X$$ ...
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### How to find an equation that warps a grid system or transforms a number line.

I am a Microbiologist with no Math background. I am looking for an equation or how to find equations that warp a normal XY plane in the Jacobian fashion. Like this https://youtu.be/CfW845LNObM?t=61 I ...
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