5 papers
Some applications of Choi polynomials of linear maps
Minh Toan Ho, Thanh Hieu Le, Cong Trinh Le +1
This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmet…
Simultaneous diagonalization via congruence of Hermitian matrices: some equivalent conditions and a numerical solution
T. H. Le, T. N. Nguyen
This paper aims at solving the Hermitian SDC problem, i.e., that of \textit{simultaneously diagonalizing via -congruence} a collection of finitely many (not need pairwise commut…
Simultaneous diagonalization via congruence of real symmetric matrices and its implications in optimization
Thi-Ngan Nguyen, Van-Bong Nguyen, Thanh-Hieu Le +1
Let be a collection of real symmetric matrices. The objective of the paper is to offer an algorithm that finds a common congruence ma…
Sum-of-square-of-rational-function based representations of positive semidefinite polynomial matrices
Thanh-Hieu Le, Nhat-Thien Pham
The paper proves sum-of-square-of-rational-function based representations (shortly, sosrf-based representations) of polynomial matrices that are positive semidefinite on some speci…
Low rank solutions to differentiable systems over matrices and applications
Thanh Hieu Le
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for fin…