Sylvester theorem for certain free modules
Sylvesterovy–Hadamardovy, Kravčukovy a Sylvesterovy–Kacovy matice
Je zcela běžné, že speciální třídy matic jsou pojmenovány podle matematika, který je buď poprvé představil nebo podstatně přispěl k jejich studiu. Článek je věnován třem třídám matic nesoucích ve svých názvech jména čtyř matematiků: Sylvesterovým–Hadamardovým maticím, Kravčukovým maticím a Sylvesterovým–Kacovým maticím. Přestože na první pohled nemají uvedené třídy příliš společného, jsou v textu ukázány jejich vzájemné souvislosti.
Symmetric matrix polynomial equations
Symmetric nonnegative realization of spectra.
Symmetric sign patterns with maximal inertias
The inertia of an by symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order . In this note we classify all the maximal inertias for symmetric sign patterns of order , and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.
Symmetric stochastic matrices with given row sums.
Characterizations of extreme infinite symmetric stochastic matrices with respect to arbitrary non-negative vector r are given.
Symmetry classes of tensors associated with the semi-dihedral groups
We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups . In particular, a necessary and sufficient condition for the existence of such a basis associated with and degree two characters is given.
Symmetry classes of tensors via semigroup operands.
System of linear equations
Systèmes de puissances partiellement divisées
Systems of four equations with a matrix application in a finite field
-forms and their properties.
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.
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...