@Article{JICS-17-047,
author = {Shi , PingLi , Nan and Lu , Xu-Chen},
title = {Analytic Solutions of a Class of Matrix Minimization Model with Unitary Constraints},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {17},
number = {1},
pages = {047--057},
abstract = {<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>},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22361.html}
}