半正定自共轭四元数矩阵平方的偏序

Partial Orderings for Squares of Positive Semidefinite Self-Conjugate Quaternion Matrices

对于Ａ，Ｂ∈Ｈ（ｎ，≥），本文给出了ＡＢ，Ａ２Ｂ２，ＡＢ＝ＢＡ之间的二推三结论，其中是Ｂａｋｓａｌａｒｙ－Ｈａｕｋｅ偏序；并且将［２］的结果完满地推广到四元数除环上．

In this paper,we give the conclusion for any two of statements AB,A 2B 2 and AB=BA imply the third statement,where A and B are a positive semidefinite self-conjugate quaternion matrix, is the Baksalary-Hauke partial ordering 3 ;and also generalized the results of the paper 2 to the quaternion field.