Related papers: 3x3 Singular Matrices of Linear Forms

We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for 0<k<10 and for even k>19. In…

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…

The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II…

We present the explicit inverse of a class of symmetric tridiagonal matrices which is almost Toeplitz, except that the first and last diagonal elements are different from the rest. This class of tridiagonal matrices are of special interest…

We study spaces of matrices coming from irreducible representations of reductive groups over an algebraically closed field of characteristic zero and we completely classify those of constant corank one. In particular, we recover the…

The inverse of the Vandermonde and confluent Vandermonde matrices are presented. In the case of the Vandermonde matrix, we present a decomposition in three factors, one of them a diagonal matrix. The evaluation of such inverse matrices is a…

We define lower triangular tensors, and show that all diagonal entries of such a tensor are eigenvalues of that tensor. We then define lower triangular sub-symmetric tensors, and show that the number of independent entries of a lower…

We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.

A result of Seymour implies that any 3-connected matroid with a modular 3-point line is binary. We prove a similar characterization for 3-connected matroids with modular 4-point lines. We show that such a matroid is either representable…

Let K be an arbitrary (commutative) field and L be an algebraic closure of it. Let V be a linear subspace of M_n(K), with n>2. We show that if every matrix of V has at most one eigenvalue in K, then dim V<=1+n(n-1)/2. If every matrix of V…

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter…

We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays. We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with hyperdeterminant 0. Our main result is an explicit formula for the 3 x 3 x 3…

We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension $n\ge 3$, extending a result by Loray, Pereira, and Touzet for degree three foliations on $\mathbb P^3$. We show that the space…

Given a $d\times d$ quasiconvex quadratic form, $d\geq 3,$ we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zero, then the form itself is an extremal quasiconvex quadratic…

We characterize the unit stable range one 2x2 and 3x3 matrices over commutative rings. In particular, we characterize the 2x2 matrices which satisfy the Goodearl-Menal condition. For 2x2 integral matrices we show that the stable range one…

Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of…

The single defining relation of the algebra of $SL_3\times SL_3$-invariants of triples of $3\times 3$ matrices is explicitly computed. Connections to some other prominent algebras of invariants are pointed out.

In this paper we consider convex improper affine maps of the 3-dimensional affine space and classify their singularities. The main tool developed is a generating family with properties that closely resembles the area function for non-convex…

This paper is about three classes of objects: Leonard triples, distance-regular graphs and the modules for the anticommutator spin algebra. Let $\K$ denote an algebraically closed field of characteristic zero. Let $V$ denote a vector space…

We show that for any $N>0$ there exists a natural even $n>N$ such that the discriminant of moduli of K3 surfaces of the degree $n$ is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the…