Related papers: Orthogonal tripotent matrices
We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…
The degeneration order of simultaneous similarity classes of $3\times 3$ nilpotent matrix tuples is determined, and is shown to be given by rank conditions.
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.
Octonion algebras over rings are, in contrast to those over fields, not determined by their norm forms. Octonion algebras whose norm is isometric to the norm q of a given algebra C are twisted forms of C by means of the Aut(C)-torsor O(q)…
The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
We axiomatize and study the matrices of type $H\in M_N(A)$, having unitary entries, $H_{ij}\in U(A)$, and whose rows and columns are subject to orthogonality type conditions. Here $A$ can be any $C^*$-algebra, for instance $A=\mathbb C$,…
Let $K$ denote an algebraically closed field with characteristic 0 and let $V$ denote a vector space over $K$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$ with diameter $d$. We say that $A,A^*$ has Krawtchouk…
In this note we characterize all regular tetrahedra whose vertices in R^3 have integer coordinates. The main result is a consequence of the characterization of all equilateral triangles having integer coordinates contained in previous work.…
We study the generic and typical ranks of 3-tensors of dimension l x m x n using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers, which is…
We consider the (symmetric) Pascal matrix, in its finite and infinite versions, and prove the existence of symmetric tridiagonal matrices commuting with it by giving explicit expressions for these commuting matrices. This is achieved by…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…
In this paper, we focus on a special class of symmetric tensors, which can be orthogonally diagonalizable, and investigate their Z-eigenpairs problem. We show that the eigenpairs can be uniformly expressed using several basic eigenpairs,…
To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results…
A tridiagonal pair is an ordered pair of diagonalizable linear maps on a nonzero finite-dimensional vector space, that each act on the eigenspaces of the other in a block-tridiagonal fashion. We consider a tridiagonal pair $(A, A^*)$ of…
This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…
We analyze the correspondence between finite sequences of finitely supported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on…
A triangular form is defined to be an integer-valued quadratic polynomial of the form $a_1P_3(x_1)+a_2P_3(x_2)+\cdots+a_kP_3(x_k)$ where $a_i's$ are positive integers and $P_3(x)=x(x+1)/2$. A triangular form is called regular if it…