Miroslav Fiedler
Encyclopedia
Miroslav Fiedler is a Czech mathematician
known for his contributions to
linear algebra
, graph theory
and algebraic graph theory
.
His article, "Algebraic Connectivity of Graphs", published in the Czechoslovak Math Journal in 1973, established the use of the eigenvalues of the Laplacian matrix
of a graph to create tools for measuring algebraic connectivity
in algebraic graph theory
. Since then, this structure has become essential to large areas of research in flocking, distributed control, clustering
and image segmentation.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for his contributions to
linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
, graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
and algebraic graph theory
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...
.
His article, "Algebraic Connectivity of Graphs", published in the Czechoslovak Math Journal in 1973, established the use of the eigenvalues of the Laplacian matrix
Laplacian matrix
In the mathematical field of graph theory the Laplacian matrix, sometimes called admittance matrix or Kirchhoff matrix, is a matrix representation of a graph. Together with Kirchhoff's theorem it can be used to calculate the number of spanning trees for a given graph. The Laplacian matrix can be...
of a graph to create tools for measuring algebraic connectivity
Algebraic connectivity
The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of...
in algebraic graph theory
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...
. Since then, this structure has become essential to large areas of research in flocking, distributed control, clustering
Clustering
Clustering can refer to the following:In demographics:* Clustering , the gathering of various populations based on factors such as ethnicity, economics or religion.In graph theory:...
and image segmentation.
External links
- Home page at the Academy of Sciences of the Czech RepublicAcademy of Sciences of the Czech RepublicThe Academy of Sciences of the Czech Republic was established in 1992 by the Czech National Council as the Czech successor of the former Czechoslovak Academy of Sciences. The Academy is the leading non-university public research institution in the Czech Republic...
.