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

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### derivative of hadamard product of

I am having difficulties to compute the derivative of the following expression: $$(xx^T)\circ A$$ with respect to $x \in R^K$ where $A \in R^{K\times K}$. Although Derivative of Hadamard ...
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I want to solve the following minimization problem: $$\underset{\alpha}{\text{min}} \; || \left( b - A(\alpha \circ x ) \right) ||_{2}^{2}$$ where $\alpha, x \in \mathbb{C}^{N}$ and $b \in \... 0answers 102 views ### relation between matrix multiplication and Hadamard product Let$\circ$denote the Hadamard product, i.e. entry-wise multiplication. Suppose we have 4 vectors$\vec{x}, \vec{y}, \vec{z}$and$ \vec{t}$be in$\mathbb{Z}^msuch that \vec{x}\circ\vec{y}=\vec{... 1answer 120 views ### Scalar-by-matrix derivative involving trace and Hadamard product I am quite new to matrix calculus, and I am trying to find the scalar-by-matrix derivative to a seemingly simple problem but have yet to find a solution online. I am trying to find \begin{align} \frac{... 1answer 176 views ### Derivative of quadratic with Hadamard product I proposed a similar question involving logarithms, but the problem is about scalar. I am trying to solve the more generalized form: \min_{\mathbf{x} \in \mathbb{R}^N_+} \left( \sum_i \left( h_i^... 0answers 160 views ### Hadamard product and tensor i'm pretty new at linear algebra, so here is my question: LetT$be a second rank tensor. Consider the next expression in basis$b$= {$b_1, b_2, b_3$}:$B$=$K\circT$There$K$is a ... 2answers 402 views ### How to compute derivative with Hadamard product? Let$\mathbf{x}$,$\mathbf{y}$and$\mathbf{z}$are$n$-dimensional column vector, and $$f = \mathbf{x}\circ \mathbf{y} \circ\mathbf{z}$$ Here$\circ$is the element-wise Hadamard product. Then how ... 0answers 40 views ### How to solve a matrix equation involving Hadamard product (Markov Chains, Average First Passage Cost) I am trying to find the average first passage cost of transition from$i$to$j$in a Markov Chain. If we consider costs of transitions as C[i,j], with the obvious property that$C[j,j]=0$, then we ... 0answers 36 views ### Expressing a matrix product of a matrix and a hadamard product as a hadamard product of matrix products I have a matrix$\mathbf{X}\in\mathbb{C}^{N\times K}$which undergoes a transform (specifically the ZCA whitening transform) represented by$\mathbf{W}\in\mathbb{C}^{N\times N}$to form$\mathbf{Y} = \...
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Multivariate vectors $\textbf{X} \sim N(0, \textbf{A})$ and $\textbf{Y} \sim N(0, \textbf{B})$ Now I want to show that $Var(\textbf{X} \odot \textbf{Y}) = \textbf{A} \odot \textbf{B}$ (Matrix) (...
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### contracting function and matrices

consider the function $$x \in \mathbb{R}^N,\quad f(x) = x \circ \frac{Cx}{x^T C x}$$ Where $C$ is a symmetric $n \times n$ real matrix positive definite and $\circ$ is the Hadamard product. Can ...
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### Hadamard product and being unitary

Let $A\in\mathbb{C}^{n\times n}$ and $A=B\circ B$ where $B$ is a unitary matrix and $\circ$ accounts for the Hadamard product. Can we say any thing about $A$ to be unitary or not?
Let $B \in \mathbb{C}^{n\times n}$ be unitarily diagonalizable such that $B=V\Lambda V^*$. Let $A=B\circ B$ where $\circ$ accounts for the Hadamard product. Then we can say that $A$ is also unitarily ...