Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence. - Danchev, Peter; García González, Esther; Gómez-Lozano, Miguel Ángel (International Linear Algebra Society, 2023)
For any n ≥ 2 and fixed k ≥ 1, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring Mn(F) to be written as a sum of an invertible matrix U and a nilpotent matrix N with Nk = 0 over an arbitrary field F.
Keywords: Grupos nilpotentes; Algebra lineal; Matrices (Matemáticas); Matrices; Nilpotents; Units; Ranks