arXiv subjects

Qing-Wen Wang

Publications and source records attributed to Qing-Wen Wang.

20 records · Page 2Linked to original sources

arXiv2016

Inequalities on generalized matrix functions

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\ B_i,\ C_i\in M_{n_i}$, $i=1,2$, and generalized matrix functions $d_χ, d_ξ$ such as the determinant and permanent, etc., we have \begin{eqnarray*}&&\left(d_χ(A_1+B_1+C_1)d_ξ(A_2+B_2+C_2)\right)^r \\ &&\hskip 1in + \left(d_χ(A_1)d_ξ(A_2)\right)^r + \left(d_χ(B_1)d_ξ(B_2)\right)^r + \left(d_χ(C_1)d_ξ(C_2)\right)^r \\ & \ge &\left(d_χ(A_1+B_1 )d_ξ(A_2+B_2 )\right)^r + \left(d_χ(A_1+ C_1)d_ξ(A_2+ C_2)\right)^r + \left(d_χ( B_1+C_1)d_ξ( B_2+C_2)\right)^r\,.\end{eqnarray*} A general scheme is introduced to prove more general inequalities involving $m$ positive semi-definite matrices for $m \ge 3$ that extend the results of other authors.

math.FA↗

arXiv2014

A simultaneous decomposition of seven matrices over real quaternion algebra and its applications

Let $\mathbb{H}$ be the real quaternion algebra and $\mathbb{H}^{n\times m}$ denote the set of all $n\times m$ matrices over $\mathbb{H}$. In this paper, we construct a simultaneous decomposition of seven general real quaternion matrices with compatible sizes: $A\in \mathbb{H}^{m\times n}, B\in \mathbb{H}^{m\times p_{1}},C\in \mathbb{H}^{m\times p_{2}},D\in \mathbb{H}^{m\times p_{3}},E\in \mathbb{H}^{q_{1}\times n},F\in \mathbb{H}^{q_{2}\times n},G\in \mathbb{H}^{q_{3}\times n}$. As applications of the simultaneous matrix decomposition, we give solvability conditions, general solutions, as well as the range of ranks of the general solutions to the following two real quaternion matrix equations $BXE+CYF+DZG=A$ and $BX+WE+CYF+DZG=A,$ where $A,B,C,D,E,F,$ and $G$ are given real quaternion matrices.

math.RA↗