Related papers: LU decomposition of totally nonnegative matrices
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
In this paper we show, using Deligne-Lusztig theory and Kawanaka's theory of generalised Gelfand-Graev representations, that the decomposition matrix of the special linear and unitary group in non defining characteristic can be made…
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.
We determine a strong form of the decomposition theorem for proper toric maps over finite fields.
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…
For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus…
A left-unilateral matrix equation is an algebraic equation of the form $$ a_0+a_1 x+a_2 x^2+... +a_n x^n=0 $$ where the coefficients $a_r$ and the unknown $x$ are square matrices of the same order and all coefficients are on the left…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.
We give a purely combinatorial algorithm for the computation of the decomposition matrices for Ariki-Koike algebras when the parameters are powers of the same root of unity. It generalizes the LLT algorithm.
Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties…
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…
The non-commutative theory of the Lebesgue-type decomposition of positive functionals is originated with S. P. Gudder. Although H. Kosaki's counterexample shows that the decomposition is not unique in general, the complete characterization…
We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
In this paper, we discuss the decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness. In fact, it is a decomposition of a Lie group into totally geodesic sub-manifolds which is different from the De…
The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.