从三个角度考察Hadamard不等式  

Make a Thorough Inquiry for Hadamard Inequality in Three Views

作　　者：咸伟志 周明亮 XIAN Weizhi;ZHOU Mingliang(Chongqing Research Institute,Harbin Institute of Technology,Chongqing 401135,China;College of Computer Science,Chongqing University,Chongqing 400044,China)

机构地区：[1]哈尔滨工业大学重庆研究院,重庆401135 [2]重庆大学计算机学院,重庆400044

出　　处：《佳木斯大学学报（自然科学版）》2024年第6期164-168,共5页Journal of Jiamusi University：Natural Science Edition

基　　金：重庆市自然科学基金面上项目(CSTB2022NSCQ-MSX0922)。

摘　　要：高等代数、数学分析以及解析几何是大学数学专业的三门基础课程,它们在理论基础、问题处理方法等方面存在差异,然而相互之间存在协同作用,相互渗透。Hadamard不等式是高等数学中一项重要的代数不等式。相较于以往单一代数视角的研究,本文旨在从高等代数、数学分析和解析几何这三门数学专业基础课程的不同视角探讨Hadamard不等式的成立,并分析在不同视角下证明该不等式的差异和联系。Advanced algebra,mathematical analysis,and analytical geometry constitute the three foundational courses in the field of university-level mathematics.They exhibit disparities in theoretical foundations and problem-solving approaches,yet they interact synergistically,permeating one another.The Hadamard inequality stands as a pivotal algebraic inequality within advanced mathematics.In contrast to previous research confined to a singular algebraic perspective,the validation of the Hadamard inequality is established through the lenses of advanced algebra,mathematical analysis,and analytic geometry–exploring the differences and connections in proving this inequality across various perspectives.

关 键 词：HADAMARD不等式 行列式 拉格朗日乘数法 欧氏空间 叉积 

分 类 号：O178[理学—数学]