Random matrix theory

Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.

James Hardy Wilkinson, 27 September 1919 - 5 October 1986

James Hardy Wilkinson was the first professional numerical analyst to be elected to the Fellowship of the Royal Society. He was without any doubt a world leader in the subject and indeed the world leader for many years in that considerable part of it generally called numerical linear algebra. But his early life could only be described as ‘humble’, and we have to thank his parents, brother and sisters and some very special schoolmasters for giving him the chance of success. In this memoir I shall call him Jim, though the nickname ‘Wilkie’ occurs in section 5.