Related papers: Sharp nonzero lower bounds for the Schur product t…

Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…

We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…

The long run behaviour of linear dynamical systems is often studied by looking at eventual properties of matrices and recurrences that underlie the system. A basic problem that lies at the core of many questions in this setting is the…

Given a $4$-dimensional vector subspace $U=\{ f_{0},\ldots,f_{3}\}$ of $H^{0}(\mathbb{P}^1 \times \mathbb{P}^1,\mathcal{O}(a,b))$, a tensor product surface, denoted by $X_{U}$, is the closure of the image of the rational map…

If a left-product $M_n... M_1$ of square complex matrices converges to a nonnull limit when $n\to\infty$ and if the $M_n$ belong to a finite set, it is clear that there exists an integer $n_0$ such that the $M_n$, $n\ge n_0$, have a common…

Let $D$ and $E$ be subspaces of the tensor product of the finite-dimensional Hilbert spaces $\mathbb{C}^m \otimes \mathbb{C}^n$. We show that the number of product vectors in $D$ with their partial conjugates in $E$ is uniformly bounded…

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows.…

Finite dimensional linear spaces (both complex and real) with indefinite scalar product [.,.] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in…

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…

We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$…

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate…

We show that, for many choices of finite tuples of generators $X = (x_1, \dots , x_d)$ of a tracial von Neumann algebra $(M, \tau)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property…

The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997. Since then the irreducibility problem for the tensor products has been open. In this paper, we…

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully…

We prove new incidence bounds between a plane point set, which is a Cartesian product, and a set of translates $H$ of the hyperbola $xy=\lambda\neq 0$, over a field of asymptotically large positive characteristic $p$. They improve recent…

We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where $\mathscr H^n$ is a Hadamard manifold.…

We introduce the Markovian matrix product density operator, which is a special subclass of the matrix product density operator. We show that the von Neumann entropy of such ansatz can be computed efficiently on a classical computer. This is…

The paper mainly deals with suprema and infima of self-adjoint operators in a von Neumann algebra $\mathcal{M}$ with respect to the spectral order. Let $\mathcal{M}_{sa}$ be the self-adjoint part of $\mathcal{M}$ and let $\preceq$ be the…

In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…

We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against…