TY - JOUR
T1 - Analytic Solutions of a Class of Matrix Minimization Model with Unitary Constraints
AU - Shi , Ping
AU - Li , Nan
AU - Lu , Xu-Chen
JO - Journal of Information and Computing Science
VL - 1
SP - 047
EP - 057
PY - 2024
DA - 2024/01
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22361.html
KW - constrained matrix minimization model, determinant function, trace function, unitary constraints.
AB - <p style="text-align: justify;">In this paper we present analytic solutions of a class of matrix minimization model with
unitary constraints as follows:$$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} \ | {\rm det}(cI_m\pm \prod\limits_{k=1}^s A_k U_k B_k W_k C_k V)|$$ $$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} |{\rm tr}(cI_m \pm \prod^s_{k=1}A_k U_K B_k W_k C_k V)| $$&nbsp;where $A_k\in C^{m\times n}$, $B_k\in C^{n\times t}$, $C_k\in C^{t\times m}$, $C^{m\times n}$ denotes $m\times n$ complex matrix set, and $c$ is a
complex number, $I_m$ denotes the $m$-order identity matrix,
det$(\cdot)$ and tr$(\cdot)$ denote matrix determinant
and trace function, respectively. The proposed results improve some existing ones in Xu (2019) [1].
Numerical examples are given to verify the validity of the theoretical results.</p>