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关于Toeplitz-Hessenberg矩阵的逆和行列式计算

The Inverse and Determinant Calculation on Toeplitz-Hessenberg Matrix
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摘要 研究了Toeplitz-Hessenberg矩阵的可逆性,并且得到它的逆是一个下三角矩阵L和一个秩1矩阵R的和.利用此结果,推导出了L和满足xy^T=R的向量x,y的公式.此外,从逆的表达式获得了其行列式的计算公式. In this paper, the reversibility of the Toeplitz-Hessenberg matrix is studied, and its inverse is the sum of a lower triangular matrix L and a rank 1 matrix R. Using this result, the formula of L and the vector x, y satisfying xy^T=R is derived. In addition, the formula of the determinant that Toeplitz-Hessenberg matrixis obtained from the inverse expression.
作者 郑振 邓勇 Zheng Zhen;Deng Yong(College of Mathematics and Statistics,Kashi University,Kashi,Xinjiang 844006,China)
机构地区 喀什大学数学与统计学院
出处 《伊犁师范学院学报（自然科学版）》 2019年第3期5-8,共4页 Journal of Yili Normal University：Natural Science Edition
关键词 HESSENBERG矩阵 TOEPLITZ矩阵 矩阵的逆 行列式 Hessenberg matrix Toeplitz matrix matrix inverse determinant
分类号 O151.21 [理学—基础数学]
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伊犁师范学院学报（自然科学版）
2019年 第3期

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