多边矩阵的块行列式Det运算  

Generalized determinant operation of multilateral matrices

作　　者：夏琪祺 罗纯 郏君乐 潘翔 马萱航 张应山 XIA Qiqi;LUO Chun;JIA Junle;PAN Xiang;MA Xuanhang;ZHANG Yingshan(School of Sciences,Shanghai Institute of Technology,Shanghai 200235,China;President's Office,Silicon Lake Vocational&Technical Institute,Kunshan 215332,Jiangsu,China;Faculty of Economics and Management,East China Normal University,Shanghai 200241,China)

机构地区：[1]上海应用技术大学理学院,上海200235 [2]硅湖职业技术学院校长办公室,江苏昆山215332 [3]华东师范大学经济与管理学部,上海200241

出　　处：《应用技术学报》2024年第4期497-506,共10页Journal of Technology

基　　金：教育部产学研合作协同育人项目(202002126022);江苏省高等教育教改研究立项重点课题(2021JSJG584)资助。

摘　　要：说明了多边矩阵的块求行列式Det运算的概念,并进一步证明了多边矩阵剖面的块求行列式Det运算的基本定理,给出了一些多边矩阵的求行列式Det运算代数性质。作为该概念的应用领域,探索了多边矩阵的块求行列式Det运算和多边矩阵的块求迹Tr运算之间的关系。The concept of block determinant Det operation of multi-lateral matrices is explained,and the basic theorem of block determinant Det operation of multi-lateral matrix section is proved.Some algebraic properties of block determinant Det operation of multi-lateral matrices are given.As the application domain of this concept,the relationship between block determinant Det operation and block tracing Tr operation of multilateral matrix is explored.

关 键 词：多边矩阵 基阵 剖分 块行列式 块迹 多边矩阵运算 

分 类 号：O13[理学—数学]