实有限可除代数间保矩阵M-P逆的共变算子对(英文)

Covariant Operators Pairs on Moore Penrose Inverses of Matrices between Various Real Finite Dimensional Division Algebras

设Ｄ，Ｄ１ 和Ｄ２ 是实有限可除代数，Ｍｍｎ（Ｄ）是Ｄ上所有ｍ ×ｎ矩阵的Ｒ线性空间． 若两个Ｒ线性算子ｆ：Ｍｍ ｎ（Ｄ１）→Ｍｍｎ（Ｄ２） 和ｇ：Ｍｎｍ （Ｄ１） →Ｍｎｍ （Ｄ２）满足ｆ（Ａ）＋ ＝ ｇ（Ａ＋ ）对于一切的Ａ∈Ｍｍ ｎ（Ｄ１）均成立，则称（ｆ， ｇ） 是一个保矩阵ＭＰ逆的共变算子对． 当ｍ ｉｎ（ｍ ， ｎ）２时，本文刻划了所有这种共变算子对（ｆ， ｇ） 的结构．

Suppose D, D 1 and D 2 are real finite dimensional division algebras. Let M mn (D) be the R linear space of all m×n matrices over D , and let f:M mn (D 1)→M mn (D 2) and g:M nm (D 1)→M nm (D 2) be two R linear operators. If f(A) +=g(A +) for all A in M mn (D 1), then we call (f,g) a Covariant Operators Pair on Moore Penrose inverses of matrices. In this paper we characterize Covariant Operators Pairs (f,g) when min (m,n)2.