Technical comment. A problem on Markov chains
A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
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 123 theorem of Probability Theory and Copositive Matrices
Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality...
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 connectivity of two trees connected by an edge of infinite weight.
The algebraic Riccati equation with Toeplitz matrices as coefficients.
The asymptotic spectrum of tensors.
The Bernoullian of a Matrix. (A Generalization of the Bernoulli Numbers)
Si associano ad una matrice infinita di un certo tipo altre due matrici dello stesso tipo, dette rispettivamente bernoulliana e antibernoulliana di A. Si studiano alcune proprietà di queste matrici. Si ottiene in tal via una generalizzazione dei classici numeri di Bernoulli.
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 Bruhat rank of a binary symmetric staircase pattern
In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
The Cauchy double alternant and divided differences.
The Cauchy problem for linear hyperbolic systems in
The Cayley transform of Banach algebras.