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### Hadamard-like product on infinitely differentiable functions

Has the following operation $*$ on formal power series $f,g$ been studied before? $$[X^n](f*g) = n! \cdot [X^n]f \cdot [X^n]g$$ where $n$ is a nonnegative integer? This is the typical Hadamard ...
• 11
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### Properties of eigenvalues and eigenvectors of a particular random matrix

Let $\mathbf{A}$ be a given $n \times m$ matrix with positive entries, and $\mathbf{B}_{n\times m}$ be a random i.i.d complex Gaussian matrix with unit variance. Assume that $\mathbf{C}$ is the ...
• 311
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### Sum of inverses of zeros of $L$-functions

Let $L(s)=\sum_{n\ge1}a(n)/n^s$ be a "standard" $L$-function, say converging for $\Re(s)>k$, having an analytic continuation with no poles to an entire function of order $1$ with functional ...
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### Solving $AXB + X\odot C = D$

I need to solve the following equation for $X$ with $d$-by-$d$ matrices $A,B,C,D$ and Hadamard product $\odot$ $$AXB + X\odot C = D$$ Vectorizing all terms gives a solution with $O(d^6)$ complexity, ...
• 2,402
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### Matrix completion problem with determinant condition?

Given two $\{0,1\}^{n\times n}$ matrices $L$ and $M$ and an integer $m$ is there a polynomial in $n$ algorithm to find a $\{-1,0,+1\}$ matrix $T$ such that $$\mathsf{det}(L+T\odot M)=m$$ where $\odot$ ...
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• 31
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### Convergence of sequence of images of Schur multipliers

Let $\eta$ be a continuous bounded function on $(0, \infty)^{2}$ so that $\eta(0,0)=1$. Let $A$ be a bounded operator on $\ell^{2}(\mathbb{Z}_{\geq 0})=\ell^{2}$ (by bounded operator I will always ...
• 31
1 vote
188 views

### References for the theory of Hadamard functions and compositions of random vectors

Recently, I fell in love with the pointwise/elementwise/componentwise/Hadamard/Schur functions and compositions of random vectors such as Hadamard squares and products of random vectors. Here is one ...
• 1,026
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### Non singularity of a generalised Vandermonde matrix through Hadamard product

I'm currently trying to prove the following. Consider $k_1,\dots,k_N$ complex numbers not lying on the real and imaginary axes. Then consider W_N(x)= \text{Wronskian}\big(\cosh(k_1x),...
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### On the notion of Hadamard rank of matrix

Given a matrix $M\in\Bbb F_2^{n\times n}$, define its Hadamard rank $h(M)$ to be the minimum number of rank $\leq2$ matrices in $\Bbb F_2^{n\times n}$ with Hadamard product (that is, the entry-wise ...
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