-forms and their properties.
Tensor complexes: multilinear free resolutions constructed from higher tensors
The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and Buchsbaum-Rim complexes, which are constructed from a matrix (i.e., a 2-tensor). The subject of this paper is a multilinear analogue of these complexes, which we construct from an arbitrary higher tensor. Our construction provides detailed new examples of minimal free resolutions, as well as a unifying view on a wide variety...
Tensor products of hermitian lattices
1. Introduction. The properties of euclidean lattices with respect to tensor product have been studied in a series of papers by Kitaoka ([K, Chapter 7], [K1]). A rather natural problem which was investigated there, among others, was the determination of the short vectors in the tensor product L οtimes M of two euclidean lattices L and M. It was shown for instance that up to dimension 43 these short vectors are split, as one might hope. The present paper deals with a similar question...
Tensor products of positive definite quadratic forms. II.
Teoría de sistemas de infinitas ecuaciones lineales y programación semi-infinita.
Ternary quartics and 3-dimensional commutative algebras.
The algebra of the subspace semigroup of
The semigroup of subspaces of the algebra of 2 × 2 matrices over a finite field is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.
The algebraic Riccati equation with Toeplitz matrices as coefficients.
The asymptotic spectrum of tensors.
The Bilinear Field of Values.
The Binet-Pexider functional equation for rectangular matrices.
The boundary of weighted analytic centers for linear matrix inequalities.
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The Cauchy double alternant and divided differences.
The Cauchy problem for linear hyperbolic systems in
The Cayley transform of Banach algebras.
The Cayley–Menger determinant is irreducible for .
The Chebyshev Solution of Certain Matrix Equations.
The Chebyshev Solution of the Linear Matrix Equation AX + YB = C.
The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value
We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue, when the edge is removed (i.e. the corresponding entry of A is replaced by 0).We show a necessary and suficient condition for each possible classification of an edge. A special relationship is observed among 2-Parter edges, Parter edges and singly...