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, mathematical structure, structure, space, Mathematica ...

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 matrix (mathemat ...

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

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 the ...

. 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 is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

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 Lap ...

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 ' is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of '. This eigenvalue is great ...

. 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 Lap ...

), 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 In mathematics, computer science, and network science, network theory is a part of graph theory. It defines networks as Graph (discrete mathematics), graphs where the vertices or edges possess attributes. Network theory analyses these networks ...

, 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 (Set (mathematics), sets of pixels). The goal of segmen ...

.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, , 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 to the Royal Bohemian Society of ...

. * {{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