Extension of Partial Diagonals of Matrices II.
Extension of Wang-Gong monotonicity result in semisimple Lie groups
We extend a monotonicity result of Wang and Gong on the product of positive definite matrices in the context of semisimple Lie groups. A similar result on singular values is also obtained.
Extensions of the Graham-Leeb-Rothschild theorem.
Extensions of the Minkowski determinant theorem
Extensions of Three Matrix Inequalities to Semisimple Lie Groups
We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.
Exterior Algebra and Projections of Polytopes.
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...
Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph
In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic...
Extremal Positive Semidefinite Forms.
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.
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...
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.
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.