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. / Mathematical Sciences / M. Sc. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/17081 |
| Date | 09 1900 |
| Creators | Khoury, Maroun Clive |
| Contributors | Botha, J. D. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (128 leaves) |
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