11 Questions

1. IMAGE readers want to hear about your career in linear algebra.  How
did you get started in this area?

It was purely accidental. In 1950 I was fired from the Royal 
Observatory, Edinburgh  because I had broken an expensive instrument the 
first time I used it. This ended my intended career as an astronomer. I 
was married with one child and the second on its way. My father offered 
to support me for Ph.D. I applied to Max Born, then the professor of 
Applied Mathematics in Edinburgh and one of the founders of quantum 
theory. But he was about to retire and was taking no more students. So I 
turned to Prof. A.C. Aitken.

2. What (a) big ideas, (b) events, and/or (c) colleagues propelled your 
research and influenced the development of your ideas?

It was again serendipity. In the fall term of 1950 Prof. Aitken gave a 
series of lectures to the small staff (faculty) of the Maths Department 
of U. Edinburgh. His theme was "Linear Operations in Probabilty", in 
effect Markov Chains in terms of stochastic matrices.   I still have my 
notes of these lectures; you can see the first page on my home page. The 
date is 17 October 1950 which I celebrate as the date of my birth as a 
research mathematician. As I have often related, one day I asked Prof. 
Aitken a question to which he replied: "Read Frobenius". I saw this as 
dismissal; it took me years to realize what excellent advice I had been 
given. 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.
I need to mention several other mathematicians who influenced me at the 
beginning of my career: Helmut Wielandt, Alexander Ostrowski, Alston 
Householder and, most of all, Olga Taussky. I am extremely grateful to 
all of them and  I am proud that they noticed my early work.

3. What were the most important events that affected your career?

Two other new mathematics Ph.D's  were hired by Queen's University, 
Belfast, when I got my first job in in 1952 (thanks to Prof. S. 
Verblunsky). They had degrees from Cambridge and Princeton. I realized 
that my education lacked training in  modern mathematics. That was the 
main motivation for pulling up my roots and moving my family to 
Wisconsin. But, surrounded as I was there by excellent mathematicians in 
subjects like functional analysis and abstract algebra, what really 
helped me was ease of contact in the U.S. with mathematicians of an 
older generation who had a background rather like mine.   



4. How has linear algebra changed in the 60 years that you have been 
involved?

It is vastly different. In the 1950s an 1960s it was generally seen as  
a dead subject which all mathematicians must know, but hardly a topic 
for research. In fact, a well known mathematician told me this to my 
face.  After I became editor in chief of LAA in 1972 I realized there 
was another way to look at the field, as an essential ingredient of many 
mathematical areas (at least during some stage of their development) and 
that this would lead to new results in linear algebra. An example of 
such an applied area active in the 1970s is control theory. Now (in 
2012)  I am amazed at the vigor of the field and new results arising 
because of connections to such applied topics as compressed sensing and 
quantum information technology. But I have a regret about one 
development. In the 1960s numerical and theoretical linear algebra 
formed a continuum and one group; now there is a split, at least in the 
U.S. Perhaps this change was inevitable.

5. What do you see as your main contributions to linear
algebra/mathematics? Can you describe the development of your main
contributions?

I have worked in several aspects of linear algebra. I think my choices 
were not determined by consideration of the importance of an area, but 
rather by an emotional need to make contributions where I felt that I 
could. I won't provide a list here. Sorry. 

But I will mention my favorite among my papers. It is a paper that links 
Lyapunov Inertia theory with Perron-Frobenius theory published in 
Numerische Mathematik in 1965.This may seem a curious choice of journal 
as the paper is not in the least computational. I used to be 
disappointed that 
this paper was hardly noticed, until a chance meeting with a young 
mathematician in the 1990s revived interest in it.

6. What do you see as the main ideas/conjectures that need to be
conquered/explored yet in linear algebra? In mathematics?

Linear Algebra is like a vast terrain with lots of hills and few high 
mountains. You cannot see all of it even if you are prepared to travel. 
I have to admit I do not have a good answer to this question.

7. Looking back, what would you have done differently in your career?
Do you regret anything in particular? What decision are you most proud
of / happy about?

I cannot speak of regret, but looking back I realize that I had several 
offers from other Universities I considered seriously and ultimately 
rejected. I sometimes wonder what would have happened to me and my 
family if I had decided differently.

8. Did you enjoy teaching?

 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. 

9. You are now 85 and still active in mathematical research. Do you see 
changes in how you do mathematics?

 I think I still have ideas of what can be explored within the 
mathematics that I am familiar with. But I now need younger coauthors to 
push through the proofs and organize the papers. I am extraordinarily 
fortunate that I have found such help.

10. You are now in your 40th and last year as editor-in-chief of Linear 
Algebra and its Applications. How do you see your role here?

The journal 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 realized 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. But I've already 
talked about this.

11. Do you have any advice for young algebraists?

 Know what you are good at, keep at it and keep at it.

I'll end with  an anecdote - a true story about a great mathematician, 
Alexander Ostrowski. Shortly after I arrived in Madison in 1959, I 
worked with Ostrowski then in his seventies. I would go to his office in 
the Mathematics Research Center at appointed times.
One day I noticed that he was studying a certain paper. So I checked it 
out and read it. Next time I went to his office I said "Professor 
Ostrowski, why are you reading this paper. It seems pretty bad to me". 
He answered "That's right. It's the first paper by a fresh Ph.D. It is 
likely to contain a good new idea which is  badly executed. There may be 
a paper in it for you!". Now there's advice!

hans   2012.03.03