Related papers: Semi-canonical binary matrices
The implicit signature k consists of the multiplication and the ({\omega}-1)-power. We describe a procedure to transform each {\kappa}-term over a finite alphabet A into a certain canonical form and show that different canonical forms have…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of…
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…
This is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters". In this paper we define the Minimal Canonical Comprehensive Groebner System (MCCGS) of a parametric ideal and fix under which…
We study the cone of completely positive (cp) matrices for the first interesting case $n = 5$. This is a semialgebraic set, which means that the polynomial equalities and inequlities that define its boundary can be derived. We characterize…
We consider systems of polynomial equations and inequalities in $\mathbb{Q}[\boldsymbol{y}][\boldsymbol{x}]$ where $\boldsymbol{x} = (x_1, \ldots, x_n)$ and $\boldsymbol{y} = (y_1, \ldots,y_t)$. The $\boldsymbol{y}$ indeterminates are…
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product.…
The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give a combinatorial classification of the faces of the…
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
This paper develops an invariant--geometric interpretation of the canonization problem for simple undirected weighted graphs based on the {discrete moving frame method} for finite groups. We consider the action of the {pair group}…
We investigate the existence of heavy columns in binary matrices with distinct rows. A column of an m x n binary matrix is called heavy if the number of ones in it is at least m/2. We introduce two recursive algorithms, A1 and A2, that…
The work considers the set $\Lambda_n^k$ of all $n\times n$ binary matrices having the same number of $k$ units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…