# Miroslav Fiedler

### Quick Info

Prague, Czechoslovakia (now Czech Republic)

Prague, Czech Republic

**Miroslav Fiedler**was a Czech mathematician who worked in linear algebra, graph theory and algebraic graph theory.

### Biography

**Miroslav Fiedler**was brought up in Prague where he attended school. His mathematical talents were clear by the time he was at secondary school and he showed these more widely by winning the mathematical problem solving competition in the journal

*Rozhledy matematicko-prirodovedecke*. After graduating from high school in 1945, Fiedler entered the Charles University of Prague to study mathematics and physics. As an undergraduate, he was taught by Bohumil Bydzovsky (born 1880) who had himself studied at the Charles University where he had been strongly influenced by his teacher and advisor Eduard Weyr. Bydzovsky's interests were mainly in geometry and he passed this love to Fiedler whom he advised while he wrote his undergraduate thesis

*Hyperosculating points of algebraic plane curves and their generalization in*$S_{r}$. For this thesis, which contained generalizations of Bydzovsky's results, Fiedler was awarded the degree of RNDr (rerum naturalium doctor) in 1950. This degree, although it is in some sense a doctorate, has a level more nearly equivalent to a Master's Degree.

Following the award of the RNDr, Fiedler undertook research at the Central Institute of Mathematics in Prague. He became a member of the first group of postgraduate students organized by Eduard Cech in the Central Institute of Mathematics. In [2], Fiedler writes:-

This group (which included Ivo Babuska, Jaroslav Hájek, Jaroslav Kurzweil, Jan Marik, Vlastimil Pták, František Sik, Otto Vejvoda, Milos Zlámal and others) would stimulate mathematical research in Czechoslovakia after a gap during the war.In 1948 a totalitarian government began to run Czechoslovakia and they closed down all the learned societies. In November 1952 the Czechoslovak Academy of Sciences was founded which served both a learned society and also as an organisation to run all the research institutes which were incorporated into it. At this time the Central Institute of Mathematics in which Fiedler was undertaking research became part of the Czechoslovak Academy of Sciences. In 1953 the Czechoslovak government brought a degree structure into the education system essentially the same as that in the USSR, so in particular the degree CSc. (Candidate of Science, essentially equivalent to a Ph.D. in standard) was introduced. The degree could be awarded by the Czechoslovak Academy of Sciences. Fiedler was already undertaking research supervised by Eduard Cech when the new degree was introduced and he became one of the first to be awarded the degree in 1955 for his thesis

*Geometry of the simplex*. He published his thesis in three parts (1954, 1955, 1956) but these were not his first publications, having already published

*Solution of a problem of Professor E Cech*(1952),

*On certain matrices and the equation for the parameters of singular points of a rational curve*(1952), and (with L Granát)

*Rational curve with the maximum number of real nodal points*(1954). Note that we give these titles in English although they were in Czech; we do the same for other titles below.

Over the next few years Fiedler's research activities were remarkable not only for the depth of the results he achieved but also for the diverse areas of mathematics in which he worked. As well as geometry, he began to study numerical methods, matrix theory and graph theory. Examples of papers he published on these topics are:

*Numerical solution of algebraic equations which have roots with almost the same modulus*(1956);

*Numerical solution of algebraic equations by the Bernoulli-Whittaker method*(1957);

*On some properties of Hermitian matrices*(1957); (with Jiri Sedlácek)

*On W-bases of directed graphs*(1958); and (with Josej Bily and František Nozieka)

*Die Graphentheorie in Anwendung auf das Transportproblem*Ⓣ (1958). In 1963 he was awarded the degree DrSc (Doctor of Sciences), the highest possible degree essentially equivalent to the habilitation in level, following a defence of his thesis. Two years later, in 1965, he was appointed as a full professor of mathematics in the Faculty of Mathematics and Physics of the Charles University of Prague. In [1] the following appreciation of his contributions is given:-

Since the early days of his research career, his favourite subjects have been geometry, graph theory, linear algebra, and their applications to numerical computations. Through 2006, he has authored or co-authored six books (two of which have been published in English) and close to 200 of papers in these and related fields (a bibliography is attached). Some of his results have shaped entire research areas, and his work has deeply influenced scientific computing in general. For many years he lectured at universities throughout the former Czechoslovakia. He always cared about talented students on the high school level - for 50 years he has been a leading figure in organizing mathematical competitions including the Mathematical Olympiad.Fiedler's impressive contributions soon gained him an international reputation and he was given invitations to lecture at many conferences and also to make longer research visits to several universities. He spent six months as a Visiting Research Mathematician at the California Institute of Technology in Pasadena, USA, in 1964, he spent the academic year 1969-70 as a Visiting Professor at Auburn University at Auburn, Alabama, USA, returning there ten years later for a six months research visit in 1979-1980. He was also a Visiting Professor at the University of South Carolina on two separate occasions spending over four months there in 1984 and again in 1987.

The above quoted appreciation mentions Fiedler's six books. The first of these books were (with Karel Culik and Vaclav Dolezal)

*Combinatorial Analysis in Practice*(1967), and (with Jaroslav Zemanek)

*Selected Problems of the Mathematical Olympiads*(1976). Next we mention

*Special matrices and their applications in numerical mathematics*published in Czech in 1981. An updated English translation appeared in 1986, with a second edition appearing in 2008. Fiedler writes in the Preface:-

In developing this book, the author has considered special matrices in the general sense and also included some more or less auxiliary topics that made it possible to present some facts or processes more demonstratively. An example is the graph theory.In 2001 he published a book which mentions three of the topics which made up his special interest in its title:

*Matrices and graphs in Euclidean geometry*(2001). Many of Fiedler's results published over the years 1985-2000 were collected together in the book

*Linear optimization problems with inexact data*(2006) which he co-authored with Josef Nedoma, Jaroslav Ramik, Jiri Rohn and Karel Zimmermann. The authors aimed their monograph at those interested in optimization, operations research, linear algebra and fuzzy sets.

Fiedler has received many honours for his contributions. In particular he received the Hans Schneider Prize from the International Linear Algebra Society:-

... for research, contributions, and achievements at the highest level of Linear Algebra.The Prize was awarded in March 1993 at a meeting in Pensacola, Florida, USA and, at the same meeting, Israel Gohberg and Shmuel Friedland received the Prize. They became the first three winners of this award. Fiedler has also been awarded, jointly with Vlastimil Pták, the National Prize of the Czech Republic in 1978. In [2] Fiedler writes about the joint work he undertook with his long-time colleague Pták:-

I should mention our results on M-matrices and P-matrices, on the theory of norms and applications in iterative processes, later on linear operators on polyhedral cones, on structured matrices (Hankel, Bézout and Loewner) and on some inequalities. We published 25 joint papers. I always enjoyed to work with Mila [the name by which Vlastimil Pták was known to his friends] and gave top priority to such work. Maybe our approaches to problems were partly complementary. Mila sought more for a theoretical point of view while I was closer to technical considerations.Fiedler was elected an honorary member of the Union of Czechoslovak Mathematicians and Physicists in 1985, received the Bernard Bolzano Gold Medal from the Czechoslovak Academy of Sciences in 1986, and the De Scientia et Humanitate Optime Meritis of the Academy of Sciences of the Czech Republic in 2006, this being the highest medal of the Academy.

### References (show)

- P Butkovic, L Hogben, R Nabben, Z Strakos and M Tuma, A brief biography and appreciation of Miroslav Fiedler with a bibliography of his books and papers,
*Linear Algebra Appl.***421**(2-3) (2007), 173-181. - M Fiedler, Vlastimil Pták (8 November 1925-9 May 1999),
*Linear Algebra Appl.***310**(1-3) (2000), 21-22. - Miroslav Fiedler [on his 70th birthday],
*Proceedings of the Prague Mathematical Conference 1996*(Icaris, Prague, 1997), ix-xi. - J Sedlácek and A Vrba, Sixty years of Professor Miroslav Fiedler,
*Czechoslovak Math. J.***36**(111) (3) (1986), 495-510. - J Sedlácek and A Vrba, Miroslav Fiedler (on the occasion of his sixtieth birthday) (Czech),
*Casopis Pest. Mat.***111**(2) (1986), 210-224. - Z Vavrín, Seventy years of Professor Miroslav Fiedler,
*Math. Bohem.***121**(3) (1996), 329-333. - Z Vavrín, Seventy years of Professor Miroslav Fiedler,
*Czechoslovak Math. J.***46**(121) (2) (1996), 369-373. - Z Vavrín, Miroslav Fiedler and Vlastimil Pták: life and work. Special issue honouring Miroslav Fiedler and Vlastimil Pták,
*Linear Algebra Appl.***223/224**(1995), 3-29.

### Additional Resources (show)

Other websites about Miroslav Fiedler:

Written by J J O'Connor and E F Robertson

Last Update November 2010

Last Update November 2010