Sums and products of square-zero matrices

Hattingh, Christiaan Johannes

dc.contributor.advisor	Botha, J. D.
dc.contributor.author	Hattingh, Christiaan Johannes
dc.date.accessioned	2018-08-02T06:09:25Z
dc.date.available	2018-08-02T06:09:25Z
dc.date.issued	2018-03
dc.identifier.citation	Hattingh, Christiaan Johannes (2018) Sums and products of square-zero matrices, University of South Africa, Pretoria, <http://hdl.handle.net/10500/24519>
dc.identifier.uri	http://hdl.handle.net/10500/24519
dc.description.abstract	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.	en
dc.format.extent	1 online resource (179 leaves)
dc.language.iso	en	en
dc.subject	Nilpotent matrix	en
dc.subject	Quadratic matrix	en
dc.subject	Square-zero matrix	en
dc.subject	Matrix division	en
dc.subject	Matrix factorization	en
dc.subject	Sum decomposition	en
dc.subject	Rational canonical form	en
dc.subject	Smith canonical form	en
dc.subject	Invariant factors	en
dc.subject	Companion matrix	en
dc.subject	Nonderogatory matrix	en
dc.subject	Matrix similarity	en
dc.subject	Matrix trace	en
dc.subject	Field	en
dc.subject	Field characteristic	en
dc.subject	Algebraic closure	en
dc.subject	Matrix polynomial	en
dc.subject.ddc	512.9434
dc.subject.lcsh	Matrices	en
dc.title	Sums and products of square-zero matrices	en
dc.type	Dissertation	en
dc.description.department	Mathematical Sciences	en
dc.description.degree	M. Sc. (Mathematics)	en