Extremal quantum states in coupled systems
Extreme Points of a Convex Subset of the Cone of Positive Semidefinite Matrices.
Extreme points of the complex binary trilinear ball
We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
Extreme preservers of maximal column rank inequalities of matrix sums over semirings
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.
Extremizing algebraic connectivity subject to graph theoretic constraints.
Facial structures of separable and PPT states
A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from...
Factorisation d'opérateurs aléatoires, d'après Benyamini et Gordon
Factorizable matrices
We study square matrices which are products of simpler factors with the property that any ordering of the factors yields a matrix cospectral with the given matrix. The results generalize those obtained previously by the authors.
Factorization Iterative Methods, M-Operators and H-Operators.
Factorization of CP-rank- completely positive matrices
A symmetric positive semi-definite matrix is called completely positive if there exists a matrix with nonnegative entries such that . If is such a matrix with a minimal number of columns, then is called the cp-rank of . In this paper we develop a finite and exact algorithm to factorize any matrix of cp-rank . Failure of this algorithm implies that does not have cp-rank . Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that...
Factorization of matrices associated with classes of arithmetical functions
Let f be an arithmetical function. A set S = x₁,..., xₙ of n distinct positive integers is called multiple closed if y ∈ S whenever x|y|lcm(S) for any x ∈ S, where lcm(S) is the least common multiple of all elements in S. We show that for any multiple closed set S and for any divisor chain S (i.e. x₁|...|xₙ), if f is a completely multiplicative function such that (f*μ)(d) is a nonzero integer whenever d|lcm(S), then the matrix having f evaluated at the greatest common divisor of and as its...
Factorizations for q-Pascal matrices of two variables
In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]
Factorizations of matrices and functions of two variables
Faktorové prostory
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
Fast computing of the Moore-Penrose inverse matrix.
Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions.
Fast solution of a certain Riccati equation through Cauchy-like matrices.
Fast Toeplitz Orthogonalization.