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Products of diagonalizable matrices

 dc.contributor.advisor Botha, J. D. dc.contributor.author Khoury, Maroun Clive en dc.date.accessioned 2015-01-23T04:24:52Z dc.date.available 2015-01-23T04:24:52Z dc.date.issued 2002-09 en dc.identifier.citation Khoury, Maroun Clive (2002) Products of diagonalizable matrices, University of South Africa, Pretoria, en dc.identifier.uri http://hdl.handle.net/10500/17081 dc.description.abstract Chapter 1 reviews better-known factorization theorems of a square 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 numbers 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 diagonalizable matrices. The next two chapters consider decomposition of singular matrices into Idempotent matrices, and of nonsingular matrices into Involutions. Chapter 5 studies factorization of a complex matrix into Positive-(semi)definite matrices, emphasizing the least number of such factors required. dc.format.extent 1 online resource (128 leaves) en dc.language.iso en dc.subject Diagonalizable factorization of matrices 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 en dc.subject.lcsh Matrices en dc.subject.lcsh Hermitian symmetric spaces en dc.subject.lcsh Positive-definite functions en dc.title Products of diagonalizable matrices en dc.type Dissertation dc.description.department Mathematical Sciences dc.description.degree M. Sc. (Mathematics) en
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