We are here [in Karviná] completely dependent on our relatives who themselves do not know how their situation will develop in the next few weeks. That is why we would be so glad to know that our child has reached safety.

We received an order to leave this country within 48 hours. This order was then changed; we may stay until 9 November. It would be our great good fortune if the matter of Hans were settled by then.

There is a mystery here; on the one hand I had very little contact with Aitken as a graduate student, on the other hand he determined much of my mathematical life of over 60 years.

This thesis is presented in support of my candidature for the degree of Ph.D. It contains work carried out at Edinburgh University between October 1950 and May 1952, under the supervision of Professor A C Aitken.

I became interested in matrices with non-negative elements when I realised that many of the most interesting algebraic properties of these matrices could be deduced when it was known which elements were positive and which were zero, the actual value of the elements being immaterial. I determined to pursue an investigation to see how far one could proceed along those lines. Though much was known about such methods, much remained, and still remains, to be done.

I had planned to give a full account of all methods used in deriving the properties of matrices with non-negative elements, and then to add some chapters of original work. It was only when I had written up a large part of my notes that I realised that this plan would make the thesis far too long. Consequently both parts of my material have had to be cut considerably. For example, I had intended to use the work of Chapter 5 to develop more fully a method used by A Ostrowski (1937) to prove the fundamental properties of matrices with non-negative elements, making use of some results in the theory of the complex variable. There was also to have been a chapter on the iteration with a square matrix $A = [a_{ij}], a_{ij} ≥ 0$, a subject which has been studied intensively when A is a "P-matrix" but very little otherwise. Some interesting theorems, not applicable to the iteration with a general matrix A, may be obtained here.

My thanks are due to my wife for help in preparing this thesis, to members of the staff and research students in the Department of Mathematics at Edinburgh University for many stimulating discussions, and particularly to Professor Aitken.

One day our doorbell rang and there stood Olga Taussky and Jack Todd who were visiting Jack's parents whose home was not far from ours. It turned out that Olga had heard of me when she visited my supervisor A C Aitken in Edinburgh. I remember little of my first meeting with Olga, but for years she would tell me I was surrounded by three small children and looked like a boy myself (at age 26). Jack has reminded me that we walked Olga and him back to his parents' house and that his father said "Bring in the wains" when he saw us.

Two other new mathematics Ph.D.'s were hired by Queen's University, Belfast, when I got my first job in 1952 (thanks to Professor S Verblunsky). They had degrees from Cambridge and Princeton. I realised that my education lacked training in modern mathematics. That was the main motivation for pulling up my roots and moving my family to Wisconsin.

When Hans was being considered for tenure in the mathematics department at the University of Wisconsin-Madison, a famous Russian algebraist was visiting. Hans was later told that this mathematician had informed a member of the tenure committee that in Russia, "we expect every mathematician to know linear algebra but it is not a field for research." Hans was rescued by members of his department who were outside his field. This incident left a deep mark on Hans, as he realised what he was up against, and made him committed to the revival of linear algebra as a field of research.

In 1967, he was elected Chair of the Mathematics Department, the second biggest in the University of Wisconsin, at the relatively early age of 39. He felt confident before this that he could deal with faculty problems, but soon regretted having taken this position, because he felt incompetent to deal with the student movement that was then sweeping North American campuses. He relinquished this position in 1969 with some relief.

I was not particularly good at teaching elementary courses to undergraduates and I did not greatly enjoy it. I liked working with my graduate students and postdocs.

... as a graduate student at the University of Wisconsin-Madison, I had the great pleasure and experience of taking a Matrix Theory class from Hans. Hans did not lecture in the typical way; he would use boards on three sides of the room to write on and would pace back and forth throughout the lecture. Initially, I was bothered that Hans didn't always write all the details of proofs. But then I quickly realised that what Hans was saying, but not necessarily writing down, was full of gems. Hans always presented a clear way of thinking about things and was able to identify the crux of an argument. I fondly remember his excitement about some results, e.g. the Perron-Frobenius theorem.

The Journal of Linear Algebra and its Applications was founded in 1968 by a group of people around Ostrowski, all associated with the Gatlinburg (now Householder) meetings. I took over in 1972 when the journal was not doing well. The turn around came when I realised that my function was not that of a guardian angel keeping out poor papers. Rather, it was to establish linear algebra as a field of research and to motivate good mathematicians to publish in the journal. The main problem was that there was (and is) much linear algebra which is seen as a sort of helpmate to other fields. It was necessary to turn this from problem to advantage. ... An example of such an applied area active in the 1970s is control theory. Now (in 2012) I am amazed at the vigour of the field and new results arising because of connections to such applied topics as compressed sensing and quantum information technology.

Hans realised that in the mathematical culture, groups tend to form around distinguished individuals. These groups flourish for a time and then typically disappear. In order to give the society permanence, a very formal structure with annual elections was established for ILAS. He wanted to make it harder to discontinue meetings in linear algebra than to continue them. Currently [in 2014] ILAS has about 400 members in more than 20 countries and publishes two journals.

Hans Schneider is one of the most influential mathematicians of the 20th century in the field of linear algebra and matrix analysis. Through his editorial guidance, rigorous teaching of applied mathematics, and development of a cohesive community of researchers, Hans Schneider has made significant contributions to the breakthroughs in robotics and the theory of stability, a theory that in turn has played an important role in everything from the economy to ecology.

The above brief biography does not amply convey the passion that Hans had for linear algebra and matrix theory, and the enormous influence that he had on the development of the field of linear algebra and on the careers of people of the linear algebra community, many of whom entered the field because of his encouragement and nurturing. He was tremendously knowledgeable about linear algebra, he had a friendly and warm personality, he had an easy approachability, and he loved to talk about mathematics, especially about nonnegative matrices. Besides his devotion to mathematics, Hans had substantial knowledge on and love of music (especially, opera), literature, and history. He was devoted to his wife Miriam and his children. We of the linear algebra community owe a tremendous debt to Hans Schneider. He is sorely missed by those of us who knew him. His inspiration and legacy will endure for many years.