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# Products of diagonalizable matrices

 dc.contributor.advisor Botha, J. D. en dc.contributor.author Khoury, Maroun Clive en dc.date.accessioned 2009-08-25T10:46:43Z dc.date.available 2009-08-25T10:46:43Z dc.date.issued 2009-08-25T10:46:43Z dc.date.submitted 0000-00-00 en dc.identifier.citation Khoury, Maroun Clive (2009) Products of diagonalizable matrices, University of South Africa, Pretoria, en dc.identifier.uri http://hdl.handle.net/10500/787 dc.description.abstract Chapter 1 reviews better-known factorization theorems of a square en matrix. For example, a square matrix over a field can be expressed as a product of two symmetric matrices; thus square matrices over real numbers can be factorized into two diagonalizable matrices. Factorizing matrices over complex num hers into Hermitian matrices is discussed. The chapter concludes with theorems that enable one to prescribe the eigenvalues of the factors of a square matrix, with some degree of freedom. Chapter 2 proves that a square matrix over arbitrary fields (with one exception) can be expressed as a product of two diagona lizab le matrices. The next two chapters consider decomposition of singular matrices into Idempotent matrices, and of nonsingutar matrices into Involutions. Chapter 5 studies factorization of a comp 1 ex matrix into Positive-( semi )definite matrices, emphasizing the least number of such factors required dc.format.extent 1 online resource (128 leaves) dc.language.iso en en dc.subject Diagonalizable factorization of matrices en dc.subject Hermitian factorization of matrices dc.subject Prescribing the eigenvalues of the factors of a square matrix dc.subject Idempotent factorization of matrices dc.subject Factorization of matrices into involutions dc.subject Positive-definite and positive-semidefinite factors dc.subject.ddc 512.9434 dc.subject.lcsh Matrices dc.subject.lcsh Hermitian symmetric spaces dc.subject.lcsh Positive-definite functions dc.title Products of diagonalizable matrices en dc.type Dissertation en dc.description.department Mathematical Sciences en dc.description.degree M.Sc. (MATHEMATICS) en
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