Ng, Zhen Chuan (2012) *Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan.* Masters thesis, University of Malaya.

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## Abstract

Let F be a field and n an integer > 2. We say that a square matrix A is persymmetric if A is symmetric in the second diagonal. Let STn(F) denote the linear space of all n x n persymmetric upper triangular matrices over F. A subspace S of STn(F) is said to be a space of bounded rank-two matrices if each matrix in S has rank bounded above by two, and a rank-two space if each nonzero element in it has rank two. In this dissertation, we classify subspaces of bounded rank-two matrices of STn(F) over a field F with at least three elements. As a corollary, a complete description of rank-two subspaces of STn(F) is obtained. We next deduce from the structural results of subspaces of bounded rank-two matrices of STn(F), a characterization of linear maps � : STn(F) ! STm(F), m > n > 2, that send nonzero matrices with rank at most two to nonzero matrices with rank at most two.

Item Type: | Thesis (Masters) |
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Additional Information: | Dissertation (M.Sc.) -- Institut Sains Matematik, Fakulti Sains, Universiti Malaya, 2012 |

Uncontrolled Keywords: | Persymmetric triangular matrices; Bounded rank-two |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Divisions: | Faculty of Science |

Depositing User: | Mrs Nur Aqilah Paing |

Date Deposited: | 17 Oct 2014 10:24 |

Last Modified: | 17 Oct 2014 10:24 |

URI: | http://studentsrepo.um.edu.my/id/eprint/4547 |

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