Miroslav Fiedler (7 April 1926 – 20 November 2015) was a Czech

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

known for his contributions to

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. ...

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

and

algebraic graph theory Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph t ...

. His article, "Algebraic Connectivity of Graphs", published in the ''Czechoslovak Math Journal'' in 1973, established the use of the

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

s of the

Laplacian matrix In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplac ...

of a graph to create tools for measuring

algebraic connectivity The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph ''G'' is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of ''G''. This eigenvalue ...

. Fiedler is honored by the '' Fiedler eigenvalue'' (the second smallest eigenvalue of the

graph Laplacian In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Lapl ...

), with its associated '' Fiedler eigenvector'', as the names for the quantities that characterize algebraic connectivity. Since Fiedler's original contribution, this structure has become essential to large areas of research in

network theory Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defi ...

, flocking, distributed control, clustering, multi-robot applications and

image segmentation In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects ( sets of pixels). The goal of segmentation is to simpl ...

.prof. RNDr. Miroslav Fiedler, DrSc.

References

External links

Home page
at the

Academy of Sciences of the Czech Republic The Czech Academy of Sciences (abbr. CAS, cs, Akademie věd České republiky, abbr. AV ČR) was established in 1992 by the Czech National Council as the Czech successor of the former Czechoslovak Academy of Sciences and its tradition goes back ...

. * {{DEFAULTSORT:Fiedler, Miroslav 1926 births 2015 deaths Mathematicians from Prague Czech mathematicians Graph theorists Recipients of Medal of Merit (Czech Republic) Combinatorialists Charles University alumni