Emeritus Professor Raymond Cuninghame-Green

By Peter Butkovic, Professor of Applied Discrete Mathematics

Emeritus Professor Raymond Cuninghame-Green (MA.,Ph.D.,D.Sc.,FBCS, FIMA), passed away on Sunday 9 June, 2013. He would have been 80 later that month.

Ray was Professor of Industrial Mathematics at the School of Mathematics in Birmingham 1975–1999 and the Head of School from 1994–1997. He laid the foundations of management mathematics at Birmingham. Ray retired in 1999 but remained research active.

Ray Cuninghame-Green is known as one of the first pioneers of max-algebra, today also known as tropical mathematics. His first paper on max-algebra was published in 1960. Ray was probably the first who realised that the maximum cycle mean is the principal max-algebraic eigenvalue of a matrix (1962).

Among his numerous other achievements let me mention for instance the analysis of max-algebraic linear systems, linear independence, rank, residuation, duality, maxpolynomials, the discovery of the characteristic maxpolynomial, rational functions and the proofs of several results for irreducible or finite matrices proved in full generality in the 1980s and 1990s by other authors, such as the complete description of (max-algebraic) eigenspaces, the cyclicity theorem or spectral projector.

Most of these appear in his publication Minimax Algebra, Lecture Notes in Economics and Mathematical Systems (Berlin: Springer, 1979). This work has been cited by hundreds of authors worldwide and contains material that is still relevant for researchers in tropical linear algebra today. A scanned copy of this work can be downloaded freely (the approval of Springer Verlag is gratefully acknowledged) from my website: http://web.mat.bham.ac.uk/P.Butkovic/max.html  

Ray was a kind, tolerant and highly respected man. He will be missed very much not only by his family but also by friends, colleagues and former students.