非奇异矩阵的高重伴随矩阵的若干性质  

Some Properties of High Degree Adjiont Matrix of Non-singular Matrix

作　　者：张艳桃[1] ZHANG Yan-tao(Business College of Shanxi University,Taiyuan,030001,China)

机构地区：[1]山西大学商务学院,山西太原030001

出　　处：《忻州师范学院学报》2018年第5期14-16,共3页Journal of Xinzhou Teachers University

摘　　要：矩阵是研究线性代数的一个重要工具。任何一个方阵都有伴随矩阵,伴随矩阵与矩阵有着密切的联系。课本上仅给出了求一次伴随矩阵的一些结论,文章着重讨论一类非奇异矩阵的高重伴随矩阵,给出了计算这类矩阵的m重伴随矩阵及其行列式的公式,然后利用逆矩阵的性质得到了计算m重伴随矩阵逆矩阵的公式,最后,推导出了m重伴随矩阵特征值的公式,并对以上公式用数学归纳法加以证明。Matrix is an important tool for studying linear algebra.We know that any square matrix has an adjoint matrix,so the adjoint matrix is closely related to the matrix.Only some conclusions about the adjiont matrix are given in the textbook.This paper focuses on the high degree adjiont matrix of non -singular Matrix,and the formula for calculating the m -adjoint matrix and its determinant of such matrices is given.Then the formula of the inverse matrix of the m -adjoint matrix is obtained by using the properties of the inverse matrix.Finally,the formula of the characteristic value of the m -adjoint matrix is deduced,and the mathematical induction method is used to prove the above formula.

关 键 词：m重伴随矩阵 特征值 非奇异矩阵 数学归纳法 

分 类 号：O151.21[理学—数学]