6 papers
A proof of the interlacing conjecture for the singular values of Sylvester-Kac matrices
Fuying Tang, Shuo Shi
Boros and Rózsa (Linear Algebra Appl. 421 (2007) 407--416) reduced the singular value problem for the odd-order Sylvester--Kac matrix to those…
Proof of Nobori's generalized Böttcher-Wenzel inequality conjecture
Shuo Shi, Juan Zhang
Let . For complex matrices , and an matrix , Nobori (Linear Algebra Appl. 725 (2025) 135--144) proposed the following conjecture on the…
A counterexample to Huang's weak majorization conjecture
Shuo Shi, Juan Zhang, Yun Zhang
We give a counterexample to a weak majorization problem, proposed by Z. Huang (Linear Algebra Appl., 434 (2) (2011) 457--462), for singular values of Hadamard products of nonnegati…
A \(3\times 3\) counterexample to Lin and Wimmer's rank-minimization conjecture associated with Roth's similarity theorem
Shuo Shi, Juan Zhang, Yun Zhang
We give a \(3\times 3\) counterexample, valid over every field, to a rank-minimization conjecture of Lin and Wimmer (Bull. Aust. Math. Soc., 84 (3) (2011), 441--443) related to Rot…
Coefficient-level output-feedback stabilization of linear port-Hamiltonian descriptor systems
Shuo Shi, Juan Zhang
This paper studies coefficient-level, structure-preserving output-feedback stabilization of linear port-Hamiltonian (pH) descriptor systems. Existing stabilization conditions gener…
Comments and extensions on "State-equivalent form and minimum-order compensator design for rectangular descriptor systems"
Shuo Shi, Juan Zhang
This technical note presents a counterexample showing that the equivalence conditions proposed by Geng et al. (IEEE Trans. Automat. Control, 2024), which use a minimum-order compen…