In Memoriam Robert C. Thompson 1931-1995

The matrix theory community was shocked and deeply saddened by the untimely death of Bob Thompson on December 10, 1995. He was awaiting a heart transplant that had recently become necessary. After growing up near Vancouver, British Columbia and receiving his bachelor’s and master’s degrees from the University of British Columbia (UBC), Bob received his Ph.D. from Caltech in 1960. He was Olga Taussky Todd’s first official student. After returning to the faculty at UBC for three years, Bob moved to the University of California at Santa Barbara (UCSB), where he spent the remainder of his career. At Santa Barbara, he began a long-term professional relationship with Marvin Marcus that included collaborative research, the founding of the journal Linear and Multilinear Algebra (now one of the three main journals of matrix theory), and the founding of the Institute for the Interdisciplinary Application of Algebra and Combinatorics. With the arrival of other prominent colleagues, including Ky Fan, Eugene Johnsen, Henryk Minc, and, later, Morris Newman, Santa Barbara became for several years the world’s mecca for research in matrix theory. During this period, Santa Barbara did much to focus attention upon the subject of matrix theory and to promote the high-level research that has been the foundation of the subject’s vigorous, world-wide renaissance. Important meetings and other special activities were hosted, and UCSB was a place for sabbaticals and other visits; assistance and inspiration were given to young researchers (such as this author), and many of the Ph.D. students trained at UCSB (Bob himself had 11) have become important contributors to the field. Several newer, strong centers of matrix research in other countries, such as Israel, Hong Kong, Portugal, and Spain, can trace their intellectual roots to Santa Barbara. Bob published more than 120 papers and a number of other items (including four undergraduate textbooks) during his career. He was serving as an editor of this journal at the time of his death. His interests were very broad and, like many researchers, his work went through stages and changes in taste, so much so that it is impossible to briefly categorize in any accurate way. Bob read a great deal of matrix theory and actually listened carefully to virtually all talks at the meetings he attended, so he knew the subject very broadly. He was often able to make helpful suggestions, even about topics on which he had no interest in working. His early work was especially algebraic, often dealing with his thesis area (a favorite of Taussky Todd’s), which was multiplicative matrix commutators (and their products) over arbitrary fields. This very detailed work answered nearly all major questions in the subject and showed a hallmark of Bob’s work: a willingness and ability to make unusually elaborate algebraic calculations in order to answer a question. It was not that he didn’t appreciate external or efficient, implicit tools if they were available. Quite the contrary--Bob was a major proponent of employing other parts of mathematics useful in matrix theory. But he almost always discovered or convinced himself of important ideas through very complicated calculations. A unifying theme of the broad middle part of Bob’s publishing career was the drive to discover and understand the exact relationship among particular fundamental matrix parameters. If necessary conditions were obvious or known, a proof of sufficiency often involved very intricate constructions. For example, Bob’s work on invariant factors, including the S-Thompson inequalities (separate papers), became very well known and attracted attention to his work in the systems and control community. This period included a major influence from and collaboration with Morris Newman, often involving number theoretic issues in integral matrices. Other examples included