摘要
针对学生学习矩阵秩的不等式比较困难的问题,综合运用演绎、分析与综合、化归的数学论证方法对秩的估计、秩的降阶及互素多项式等方面的重要不等式进行研究,并举例说明这些不等式在分块矩阵、线性方程组及判断线面位置关系等问题中的应用,这将有助于学生更好地掌握矩阵的基本理论,提高学生的抽象思维能力和逻辑思维能力。
To solve students’difficulties in learning inequalities of matrix rank,the author studied several important inequalities concerning the rank estimation,rank reduction and relatively prime polynomials were studied.Furthermore,the application of these inequalities in block matrix,linear equations and judging the positional relationship between lines and planes was illustrated with examples.
作者
黄述亮
HUANG Shu-liang(School of Mathematics and Finance,Chuzhou University,Chuzhou 239000,China)
出处
《辽东学院学报（自然科学版）》
CAS
2021年第1期61-65,共5页
Journal of Eastern Liaoning University:Natural Science Edition
基金
滁州学院校级教学研究重点项目(2020jyz004)。
关键词
矩阵的秩
初等变换
齐次线性方程组
matrix rank
elementary transformation
system of homogeneous linear equations
