从三个角度考察Hadamard不等式

Make a Thorough Inquiry for Hadamard Inequality in Three Views

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.