Related papers: Untriangular factorization of holomorpic symplecti…
Hadamard matrices are square $n\times n$ matrices whose entries are ones and minus ones and whose rows are orthogonal to each other with respect to the standard scalar product in $\Bbb R^n$. Each Hadamard matrix can be transformed to a…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
We identify and analyse obstructions to factorisation of integer matrices into products $N^T N$ or $N^2$ of matrices with rational or integer entries. The obstructions arise as quadratic forms with integer coefficients and raise the…
Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
We show that, for a certain class of partitions and an even number of variables of which half are reciprocals of the other half, Schur polynomials can be factorized into products of odd and even orthogonal characters. We also obtain related…
This work provides a quaternioinc reprsentation for real symplectic matrices in dimension four, analogous to the pair of unit quaternions representation for special orthogonal matrices. In the process of finding formulae for this…
The randomised Horn problem, in both its additive and multiplicative version, has recently drawn increasing interest. Especially, closed analytical results have been found for the rank-1 perturbation of sums of Hermitian matrices and…
We first summarize joint work on several preliminary canonical Lambert series factorization theorems. Within this article we establish new analogs to these original factorization theorems which characterize two specific primary cases of the…
We study matrix integrals of the form $$\int_{\mathrm{USp(2n)}}\prod_{j=1}^k\mathrm{tr}(U^j)^{a_j}\mathrm d U,$$ where $a_1,\ldots,a_r$ are natural numbers and integration is with respect to the Haar probability measure. We obtain a compact…
We develop a holomorphic equivalence between on one hand the space of pairs (stable bundle, flat connection on the bundle) and the "sheaf of holomorphic connections" (the sheaf of splittings of the one-jet sequence) for the determinant…
Let $V$ be a vector space with countable dimension over a field, and let $u$ be an endomorphism of it which is locally finite, i.e. $(u^k(x))_{k \geq 0}$ is linearly dependent for all $x$ in $V$. We give several necessary and sufficient…
We consider the problem of convergence to zero of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to a suitable choice of matrices $\{B_{i}\}$. It is…
Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…
A novel method to obtain parametrizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via…
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…