Sums and Products of Square-Zero Matrices

The Square-Zero Basis of Matrix Lie Algebras

“…Square-zero matrices have been dealt with in several settings and with different purposes; for example, see [2], [3], [4], [8], [10], [13], among other authors. Below, we consider such matrices in connection with the following question:…”

“…For the sake of simplicity we call this class in the sequel, SQZ-LA class. Square-zero matrices have been dealt with in several settings and with different purposes; for example, see [8][9][10][11][12][13], among other papers and authors.…”

Sums of square-zero endomorphisms of a free module

“…More than that, it is known that every matrix with zero trace is a sum of four square-zero matrices [7,10]. Also, the problem of describing the set of sums of two (or three) square-zero matrices has attracted a significant amount of attention [1,3,9]. Another direction of research is the study of bounded operators over Hilbert spaces [2,5,10,11].…”