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Abstract

Much is known about the eigenvalues of some special types of matrices. For example, the eigenvalues of a hermitian or skew-hermitian matrix lie on a line while those of a unitary matrix lie on a circle; their spectra are "linear" or "circular". This suggests the question: What matrices have this property? Or, more generally, what matrices have their eigenvalues on plane curves of a simple kind? Is it possible to recognize such matrices by inspection? In this thesis, we make a small start on these problems, exploring some matrices whose eigenvalues lie on one or more lines, or on one or more circles.