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1	Sums and products of square-zero matrices Hattingh, Christiaan Johannes 03 1900 (has links) Which matrices can be written as sums or products of square-zero matrices? This question is the central premise of this dissertation. Over the past 25 years a signi - cant body of research on products and linear combinations of square-zero matrices has developed, and it is the aim of this study to present this body of research in a consolidated, holistic format, that could serve as a theoretical introduction to the subject. The content of the research is presented in three parts: rst results within the broader context of sums and products of nilpotent matrices are discussed, then products of square-zero matrices, and nally sums of square-zero matrices. / Mathematical Sciences / M. Sc. (Mathematics) Nilpotent matrix Quadratic matrix Square-zero matrix Matrix division Matrix factorization Sum decomposition Rational canonical form Smith canonical form Invariant factors Companion matrix Nonderogatory matrix Matrix similarity Matrix trace Field Field characteristic Algebraic closure Matrix polynomial 512.9434 Matrices