UM ETheses Collection (澳門大學電子學位論文庫)
 Title

Numerical ranges and spectrum of product of matrices
 English Abstract

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Let A be any n × n complex matrix. Let σ(A), W(A), and W0 (A) denote respectively the spectrum, the numerical range and the angular numerical range of A. For product of matrices, there are many inclusion results between the three sets. In particular, (i) if A is a multiple of a positive semidefinite matrix, then σ(AB) ⊆ W(A)W(B) for all n × n complex matrices B; (ii) if 0 6∈ W(A), then σ(AB) ⊆ W0 (A)W0 (B) for all n × n complex matrices B. In this thesis, we consider the converse of these results. For any fixed A, we find the necessary and sufficient conditions for the above inclusions to hold for all n × n complex matrix B. Some other inclusion relations between numerical range and angular numerical range are also considered.
 Issue date

2013.
 Author

Gao, Yuan
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Matrices
Numerical range
Spectrum analysis  Mathematics
 Supervisor

Cheng, Che Man
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991004679449706306