Related papers: Results about persymmetric matrices over F_2 and r…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…
The problem of finding the maximal dimension of linear or affine subspaces of matrices whose rank is constant, or bounded below, or bounded above, has attracted many mathematicians from the sixties to the present day. The problem has caught…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
We determine the probability that a random n x n symmetric matrix over {1, 2, ... , m} has determinant divisible by m.
The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ rank-one matrices of a specific form. We provide estimates for the eigenvalues and eigenvectors. When the condition number of the initial matrix tends…
We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $\mathbb{R}^d$ generate high…
In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for $2\times ... \times 2$ tensors and for tensors of small…
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
In this work an efficient algorithm to perform a block decomposition (and so to compute the rank) of large dense rectangular matrices with entries in $\mathbb{F}_2$ is presented. Depending on the way the matrix is stored, the operations…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…