Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence.
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International Linear Algebra Society
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Abstract
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.
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Danchev, Peter & García, Esther & Lozano, Miguel. (2023). Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence. The Electronic Journal of Linear Algebra. 39. 460-471. 10.13001/ela.2023.7851.
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