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Products of diagonalizable matrices

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dc.contributor.advisor Botha, J. D. Khoury, Maroun Clive en 2015-01-23T04:24:52Z 2015-01-23T04:24:52Z 2002-09 en
dc.identifier.citation Khoury, Maroun Clive (2002) Products of diagonalizable matrices, University of South Africa, Pretoria, <> en
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 M. Sc. (Mathematics) en

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