# Tagged Questions

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### Derivative of $f(x)=\|Ax\|_2^2$

I'm trying to find the derivative of $f(x)=\|Ax\|_2^2$ where $A$ is some matrix and $\|u\|_2$ is the euclidean norm of $u$, $\|u\|_2 = \sqrt{u_1^2+u_2^2+\cdots+u_n^2}$ I know how to do this by ...
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### derivative of 2 norm wrt matrix

I have a matrix A which is of size m,n, a vector B which of size ...
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### gradient norm of a simple function

In this answer Derivation of soft thresholding operator how can I derive that $\nabla(||x-b||_2^2)=b-x$?
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### Proving that derivative of a bounded linear map (at a point) is the map itself

I have been struggling to prove a claim. How can I show that If $f:X \rightarrow Y$ is a bounded linear map, then $Df(x)=f$ for all $x \in X$? Attempt: $f:X \rightarrow Y$ is a bounded linear map ...
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### Check my answer - Finding the jacobi matrix of a function

We are given $f: \mathbb R^n \to \mathbb R^n$ such that: $0 \neq x \in \mathbb R^n$, $f(x)=\frac{x}{|x|}$, where $|x| = \sqrt {x_1^2 +x_2^2+...+x_n^2}$ Find the jacobi matrix (the differential ...
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### Derivative of function that includes norm

I was solving the problem: find the derivative of a function f : H → R, $f (x) = \sin ||x||^3$ (H is Hilbert space). I got the answer $f'(x)=3\cos||x||^3 x||x||$. Is this correct or I am doing ...
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### Gradient of a norm with a linear operator

In mathematical image processing many algorithms are stated as an optimization problem, where we have an observation $f$ and want recover an image $u$ that minimizes a objective function. Further, to ...
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### Calculate the derivative of a complex norm

I'm stuck with a rather trivial looking question. How do you calculate the derivative of the norm of a complex number to it self? Like in $$\frac{d|a|^2}{da} = ?$$ I think it would give rise to a ...
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### Methods of computing the derivative of vector norms

I am very new to norms. Except the basic definitions and properties of the norm, I don't know too much about it. Now, I am very interested in computing the derivative of the norms. So, I am wondering ...
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### Matrix $L_1$ norm derivative [duplicate]

Say that $A\in \mathcal{M}_{n,n}$ what is the result of the following derivative: $\frac{\partial \|A- diag(A)\|_1}{\partial A}$, where $diag(A)$ is the matrix that contains the diagonal entries of ...
I read in a paper called "Characterization of the subdifferential of some matrix norms" that it defines the subdifferential of the matrix norm like this: \partial ||A||=\{G \in R^{m\times n} : ...
I'd like to find the gradient of $\frac{1}{2} ||X A^T||_F^2$ with respect to $X_{ij}$. Going by the chain rule in the Matrix Cookbook (eqn 126), it's something like \$\partial \left[\frac{1}{2} ||X ...