关于分块三角矩阵的几个行列式不等式

Determinantal inequalities for block triangular matrices

设T=éê X0 YZù ú是n阶级分块矩阵,X和Z分别是r级矩阵和n-r级方阵。Lin证明了一个有趣的行列式不等 式,det(In+T*T)≥det(Ir+X*X) det(In-r+Z*Z)。利用 Hadamard积和复合矩阵的性质,本文证明了上述不等式关于 Had- amard 积的模拟不等式,即涉及 Hadamard 积的行列式不等式。

LetT= éêX0 YZ ùú be an n -square matrix, in which X and Z are r -matrix and n-r square matrix, respectively. Lin provedthatdet(In+T*T)≥det(Ir+X*X) det(In-r+Z*Z).ThispaperpresentananalogousinequalityinvolvingtheHadamardprod- uct by using the properties of Hadamard product and compound matrix.