On decomposing any matrix as a linear combination of three idempotents

Matrices over a commutative ring as sums of three idempotents or three involutions

Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results \cite{de} on decomposing every matrix over a field of positive characteristic as a sum of idempotent matrices, we address decomposing every matrix over a commutative ring as a sum of three idempotent matrices and, respectively, as a sum of three involutive matrices.

关于任意域上两个幂等矩阵的线性组合

On linear combinations of two idempotent matrices over an arbitrary field

给定任意域K和非零标量a，b，给出了M_n（K）中矩阵A是系数为a，b的两个幂等元的线性组合的充要条件.这扩展了哈特维希和普查以前得到的结果在两个方面：这里考虑的字段K是任意的（可能的特征2），并考虑到的情况a是不同的b和-b。