Contractive Matrices of Hua Type
Linear and Multilinear Algebra
Contractions, Contractive matrices, Determinant inequalities, Eigenvalues, Elementary symmetric functions, Hua's determinant inequality, Hua's matrix inequality, Matrix inequalities, Positive semidefinite matrix
This is continuation of the recent work by Xu, Xu and Zhang [Revisiting Hua–Marcus–Bellman–Ando inequalities on contractive matrices, Linear Algebra Appl. 430 (2009), pp. 1499–1508] on contractive matrices. We study the relations of block matrices of Hua type, present some properties that the eigenvalues of Hua matrices possess, especially for the 2 × 2 block case, discuss the analogues for higher dimensions and estimate the closeness of two Hua matrices. At the end, we propose a conjecture on the eigenvalues of Hua matrices and an open problem on the symmetric functions of the eigenvalues of contractive matrices.
Xu, Guanghui; Xu, Changqing; and Zhang, Fuzhen, "Contractive Matrices of Hua Type" (2011). Mathematics Faculty Articles. 47.