摘要
0 引言和记号用简便的方法来判定矩阵的奇异性,且在非奇的情况下估计出行列式的下界,这在实际问题中具有重要用途.这个下界表征了矩阵的非奇异度,且在其他许多估计式中也常用到,比如矩阵特征值下界的估计就与行列式下界的估计密切相关.Ostrowski,石钟慈,王伯英对于对角占优矩阵的行列式的下界进行了讨论.本文取消对角占优条件,给出几类范围更广的矩阵的行列式的下界估计,且与文献[3]的结果互不包含. 设A=(aij)∈Cm×n若|aii|≥∧i（A）,i∈N≡{1,…,n} ,其中∧i（A）≡∑|a（ij）|,则称A为对角占优阵,记为A∈D0。
In order to judge whether a matrix is singular or not, the simple way is to estimate the lower bound of the determinant for the matrix. This lower bound characterizes the degree of non-singularity and is also closely related to the lower bound of the eigenvalues for the matrix. Available results are mainly for diagonal predominant matrices. The authors concerned matrices which are not diagonal predominant, gave the lower bound estimates of determinants for much wider range of matrices. The new theorems were strictly proven in the paper. The applicability to matrices was greatly extended.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
1992年第5期111-114,118,共5页
Journal of Xi'an Jiaotong University
关键词
矩阵
行列式
下界
Linear algebra
Mathematical techniques
