Related papers: Some notes about matrices, 4
Given a tract $F$ in the sense of Baker and Bowler and a matrix $A$ with entries in $F$, we define several notions of rank for $A$. In this way, we are able to unify and find conceptually satisfying proofs for various results about ranks of…
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
We construct explicit Boolean square matrices whose rectifier complexity (OR-complexity) differs significantly from the complexity of their complement matrices.
We discuss complex rephasing invariants of charged lepton and neutrino mass matrices and associated theorems which determine in general (i) the number of physically meaningful phases in these matrices and (ii) which elements of these…
In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra…
In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices.…
This note presents explicit formulae for the exponentials of a wide variety of matrices which are 4x4, anti-Hermitian. Easily verifiable conditions characterizing when such matrices admit one of three minimal polynomials are also given.…
It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…
Some explicit expressions are given for the theta series of Niemeier lattices. As an application, we present some of their congruence relations.
This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.
A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…
These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.
We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be…
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…
Motivated by the recent work of R. Casals on binary invariants for matrix mutation, we study the matrix congruence relation on quasi-Cartan matrices. We obtain a classification and determine normal forms modulo 4. We also establish their…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…