For questions about Hadamard product between two matrices, or it can concern analytic functions.

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### "Leave-on-out Correlation" between Matrices

I'd like to enforce a special constraint in my optimization problem. The solution to my problem is a set of matrices $Q_1, ..., Q_N \in \mathbb{R}^{G \times K}$ and I'd like to make sure that: For ...
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How can I compute the following derivative? $$\frac{\partial(K u \circ T u)}{\partial u}$$ $K$ and $T$ are constant matrices, $u$ is an unknown vector. and $\circ$ is Hadamard product. my solution: $$\... 0 votes 1 answer 38 views ### Computation of two Jacobians Definitions Consider the following function f:\mathbb{R}^N\mapsto\mathbb{R^2} \begin{equation*}f(\ell_{k+1})= \left[\begin{array}{c} v_{k+1}\,\cos(h_{k+1})\\ v_{k+1}\,\sin(h_{k+1}) \end{array}\... 2 votes 1 answer 78 views ### Inverse of matrix with hadamard product Let A and B, X be matrices with \mathbb{R}^{n \times n} where A, B are a dense and sparse matrix, i.e., the almost elements of B are zeros, respectively. I'm looking for a way to solve ... 3 votes 1 answer 103 views ### Lower bound on smallest eigenvalue of hadamard product of two Hermitian matrix Let A and B be n \times n real symmetric matrix. Suppose A is positive definite and denote its smallest eigenvalue as \lambda_{\min}(A)>0. All elements of B are positive and bounded, i.e. 0\le ... 0 votes 0 answers 56 views ### Maximum of the permanent of the Hadamard product between a unitary matrix and its permuted matrix The problem is to$$\max_{U}\left|\operatorname{perm}\left(U\circ U_{\sigma}\right)\right|$$where U=(u_{i,j}) is an n\times n unitary matrix and U_{\sigma}=(u_{i,\sigma(j)}) is its permuted ... 0 votes 2 answers 66 views ### Matrix operation to exponentiate each element in a vector I am using the following matrix algebra to obtain a vector, however, I eventually need all the resulting elements to be exponentiated. \begin{equation} \begin{split} \boldsymbol{\beta}^{\textsf{T}}\... 0 votes 0 answers 46 views ### Conditional convergence of the Hadamard product The product$$\prod_\rho \left(1-\frac{s}{\rho}\right)$$where \rho ranges over all zeros of the Riemann zeta function is often referred to as the Hadamard product (because its convergence was first ... 0 votes 1 answer 26 views ### How to find the gradient of matrix multiplying hadamard product [closed] I'm trying to find the gradient of A(x∘x) with respect to x, where ∘ is the Hadamard product and A is a matrix with positive real values. Thanks in advance! 0 votes 0 answers 10 views ### Hadamard product of two non-zero vectors with infinite and zero elements Did anybody ever define (generalize) the Hadamard product of two non-zero vectors \mathbf{a}\circ \mathbf{b}=\mathbf{c} in such a way that if a_n=0 and b_n=\infty, then c_n=e^{-\gamma}? For ... 1 vote 1 answer 69 views ### Upper-bound for nuclear norm of A \circ (v \otimes v) in terms of operator norm (or nuclear norm) of matrix A and L_\infty-norm of vector v. Let A \in \mathbb R^{n \times } be a psd matrix such that \|A\|_{op} \le r_1 and \|A\|_{*} \le r_2. Let v \in \mathbb R^n such that \|v\|_\infty \le r_3. Let B:=A \circ V be the Hadamard ... 0 votes 1 answer 201 views ### Chain rule and derivative with matrix product? I'm trying to compute some derivatives with given vectors and functions: column vector X=[x_1,x_2,\dots,x_n ]^T and Z=[z_1,z_2,\dots,z_n ]^T, row vector Y=[y_1,y_2,\dots,y_n ] f(X,Y)=e^{XY}$$...
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0I have a linear map $f:\mathbb{R}^{n\times m}\to \mathbb{R}^{n\times m}$ defined as $$f(X) = A \odot X \qquad \qquad \text{ for some } A\in\mathbb{R}^{n\times m}$$ where $\odot$ is the Hadamard ...
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### Convex sets of matrices

I am looking for any information about matrix sets $S$ that verify the following convexity property: $A, B \in S, 0 \leq \lambda \leq 1 \implies [A(i,j)^{1-\lambda} B(i,j)^\lambda]_{ij} \in S$. Do ...
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### Hadamard Product inside a norm

Is it true to say $\|A\circ B\| \le \|A\| \|B\|$? $\circ$ is the Hadamard product.
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### Differentiating an expression involving Hadamard Product

I'm trying to calculate $\frac{dY}{dW}$ where: $$Y = (W^TX)oC$$ 'o' denotes the hadamard product. W, X and C are matrices with dimension (d, c), (d, n) and (c, n) respectively. From matrix cookbook:,...
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### Can you rearrange this simple Hadamard & Matrix product?

I have the following matrix operation: ${((AB^T) \odot C)D}$ where juxtaposition denotes the matrix product and $\odot$ the Hadamard product. A, B & D are all matrices of shape (3, 2) and C is a ...