H上半正定广义逆A{i,…,j;≥}的半正定偏序解

Positive Semidefinite Partial Order Solutions for Positive Semidefinite Generalized Inverses A{i, …,j; ≥} over H

在文献〔1—2〕基础上,本文考察了半正定自共轭四元数矩阵A的半正定(i,…,j)—逆A{i,…,j;≥}中的半正定偏序解问题,证明了各广义逆的半正定偏序解的显公式。

In this paper the problems of the positive semidefinite partial order in the positive semidefinite generalized inverses A { i, …, j; ≥} of a positive semidefinite self-conjugate matrix A of quaternions are discussed, and their corresponding explicit solutions are proved.