一个实数域上不等式在矩阵理论中的拓展形式
Generalization of a Real Inequality in Matrix Theory
摘要: 本文以实数基本二次不等式为核心， 将其严格推广至复方正规矩阵范畴， 依托谱分解定理与Frobenius范数百不变性，系统建立迹不等式、单矩阵范数不等式、乘积型广义不等式、加权不等式及多矩阵和式不等式，形成完整推广链条。
Abstract: Taking the fundamental quadratic inequality over real numbers as the starting point,this paper rigorously generalizes it to the class of complex normal matrices. Based on the spectral decomposition theorem and the unitary invariance of the Frobenius norm, we systematically establish a series of inequalities including trace inequalities, single- matrix norm inequalities, generalized product-type inequalities, weighted inequalities and sum inequalities for multiple matrices, which constructs a complete generalization framework.
文章引用：李雪娇, 吴佳浩, 海泽琦, 阿尔孜古丽·阿布来提, 何奇, 蔡学鹏. 一个实数域上不等式在矩阵理论中的拓展形式[J]. 应用数学进展, 2026, 15(9): 81-87. https://doi.org/10.12677/AAM.2026.159375

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