A note on sums of three square-zero matrices

作者：Pazzis Clement de Seguins^*

来源：Linear and Multilinear Algebra, 2017, 65(4): 787-805.

DOI：10.1080/03081087.2016.1202187

• Decomposition
• rational canonical form
• square-zero matrices
• fields with characteristic 2
• idempotent matrices

It is known that every complex trace-zero matrix is the sum of four square-zero matrices, but not necessarily of three such matrices. In this note, we prove that for every trace-zeromatrix A over an arbitrary field, there is a non-negative integer p such that the extended matrix A circle plus 0(p) is the sumof three square-zeromatrices (more precisely, one can simply take p as the number of rows of A). Moreover, we demonstrate that if the underlying field has characteristic 2 then every trace-zero matrix is the sum of three square-zero matrices. We also discuss a counterpart of the latter result for sums of idempotents.

• 出版日期2017