The life and work of Fergus Gaines ( 1939 – 2001 )

Fergus was born and brought up in Dublin. After attending O'Connell Schools he came to UCD (University College Dublin) in 1957 where he completed a B.Sc. degree followed by an M.Sc. degree in Mathematical Science. He spent the year 1961-62 as a lecturer in UCD before spending four years in California studying for a doctorate at Caltech (California Institute of Technology). He carried out this research under the supervision of Olga Taussky-Todd, the distinguished matrix theorist and number theorist. Olga used to refer to Fergus as her " ideal graduate student ". She paticularly liked him for his good humour, positive outlook, pleasant personality, diligence and honesty. After obtaining his Ph.D. in 1966 Fergus returned to Ireland and spent the rest of his career in the Department of Mathematics in UCD. He retired in September 2000 from his full-time post as Senior Lecturer in Mathematics but continued to lecture on a half-time basis until his untimely death in November 2001. Fergus made a number of significant contributions to the algebraic theory of matrices, both in his thesis and in subsequent papers. His refereed papers have been almost exclusively in the area of matrix theory. In 1936 McCoy [13] proved that if A 1 , A 2 , ......, A k are n × n complex matrices then there exists an invertible n × n matrix T such that the matrices T −1 A i T are upper triangular for all i = 1, 2, ...., k if and only if p(A 1 , z k. This theorem has served as motivation for much research work and important extensions have been obtained by Olga Taussky and her collaborators and students, including Fergus, as well as many other authors. Given a set of n × n matrices over a field , a classic problem is that of determining the structure of the algebra which they generate. McCoy's theorem essentially characterizes the case when A is commutative