Abstract
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.
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