两个重要的秩不等式的推广及其应用  

Generalizations and applications of two important rank inequalities

作　　者：郑鹭 严慧 周静[1] ZHENG Lu;YAN Hui;ZHOU Jing(Teaching Section of Mathematics,Hubei Engineering Institution,Huangshi 435002,China;School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北工程职业学院数学教育部,湖北黄石 [2]湖北师范大学数学与统计学院,湖北黄石

出　　处：《湖北师范大学学报(自然科学版)》2025年第1期1-11,共11页Journal of Hubei Normal University:Natural Science

摘　　要：利用矩阵的值域、零空间和分块矩阵的初等变换推广了两个著名的秩不等式,Sylvester秩不等式和Frobenius秩不等式。给出了这两个推广的秩不等式中等号成立的一些充要条件。运用这些充要条件得出了它们在一些秩等式上的应用。This paper generalized two famous rank inequalities using range space,null space and element transformations of block matrices,Sylvester rank inequality and Frobenius rank inequality.Moreover,it proposed some necessary and sufficient conditions for the generalized Sylvester rank inequality and Frobenius rank inequality to become an equation.In addition,it utilized these results to provide applications in rank equality.

关 键 词：Sylvester秩不等式 Frobenius秩不等式 值域 零空间 初等变换 

分 类 号：O152.2[理学—数学]