Miroslav Fiedler | Academic Influence

Miroslav Fiedler's AcademicInfluence.com Rankings

Miroslav Fiedler

Mathematics

#1659

World Rank

#2670

Historical Rank

Measure Theory

#473

World Rank

#672

Historical Rank

mathematics Degrees

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Mathematics

Miroslav Fiedler's Degrees

PhD Mathematics Charles University

Why Is Miroslav Fiedler Influential?

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According to Wikipedia, Miroslav Fiedler was 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. Fiedler is honored by the Fiedler eigenvalue , 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, flocking, distributed control, clustering, multi-robot applications and image segmentation.

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Miroslav Fiedler's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Algebraic connectivity of graphs (1973) (3776)
A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975) (1146)
On matrices with non-positive off-diagonal elements and positive principal minors (1962) (821)
Special matrices and their applications in numerical mathematics (1986) (440)
Linear Optimization Problems with Inexact Data (2006) (349)
Some generalizations of positive definiteness and monotonicity (1966) (221)
Laplacian of graphs and algebraic connectivity (1989) (198)
Eigenvectors of acyclic matrices (1975) (197)
Matrix Inequalities (1966) (180)
Eigenvalues of Nonnegative Symmetric Matrices (1974) (152)
Bounds for the determinant of the sum of hermitian matrices (1971) (145)
Spectral radius and Hamiltonicity of graphs (2009) (115)
A note on companion matrices (2003) (115)
Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices (1974) (88)
Diagonally dominant matrices (1967) (86)
Completing a Matrix When Certain Entries of Its Inverse Are Specified (1986) (82)
Geometry of the numerical range of matrices (1981) (75)
Hankel and loewner matrices (1984) (73)
A characterization of tridiagonal matrices (1969) (71)
An inequality for the hadamard product of an M-matrix and an inverse M-matrix (1988) (63)
A new positive definite geometric mean of two positive definite matrices (1997) (57)
Absolute algebraic connectivity of trees (1990) (51)
A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix (1985) (50)
Bounds for eigenvalues of doubly stochastic matrices (1972) (48)
Generalized norms of matrices and the location of the spectrum (1962) (40)
Expressing a polynomial as the characteristic polynomial of a symmetric matrix (1990) (33)
Ultrametric sets in Euclidean point spaces (1998) (33)
Numerical range of matrices and Levinger's theorem (1995) (31)
A characterization of the Moore-Penrose inverse (1993) (31)
Cyclic products and an inequality for determinants (1969) (30)
Analytic functions of M-matrices and generalizations (1983) (29)
Notes on Hilbert and Cauchy matrices (2010) (28)
SOME CHARACTERIZATIONS OF SYMMETRIC INVERSE M-MATRICES (1998) (27)
Consecutive-column and -row properties of matrices and the loewner-neville factorization (1997) (27)
Complementary basic matrices (2004) (26)
Polyhedral cones and positive operators (1974) (25)
Structure ranks of matrices (1993) (25)
A Geometric Approach to the Laplacian Matrix of a Graph (1993) (25)
Matrices and Graphs in Geometry (2011) (24)
Theory of graphs and its applications : proceedings of the symposium held in Smolenice in June 1963 (1964) (24)
Some results on matrices of class $K$ and their application to the convergence rate of iteration procedures (1966) (23)
Notes on inverse M-matrices (1987) (23)
Some minimax problems for graphs (1993) (22)
Relations between the diagonal elements of two mutually inverse positive definite matrices (1964) (22)
A classification of matrices of class Z (1992) (22)
Extreme Operators on Polyhedral Cones (1976) (21)
Characterizations of sign patterns of inverse-positive matrices (1981) (20)
Remarks on the Schur complement (1981) (20)
Cones which are topheavy with respect to a norm (1973) (19)
Rank-preserving diagonal completions of a matrix (1987) (19)
Pencils of real symmetric matrices and real algebraic curves (1990) (19)
A characterization of the closure of inverse M-matrices (1988) (19)
Polynomials and Hankel matrices (1985) (19)
Special Ultrametric Matrices and Graphs (2000) (18)
Quasidirect Decompositions of Hankel and Toeplitz Matrices (1984) (17)
Bézoutians and intertwining matrices (1987) (16)
A note on the Hadamard product of matrices (1983) (15)
On inverting partitioned matrices (1963) (15)
Elliptic Matrices With Zero Diagonal (1994) (15)
Classes of products of M-matrices and inverse M-matrices (1983) (15)
Diagonals of convex sets (1978) (14)
Intrinsic products and factorizations of matrices (2008) (13)
Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity (1992) (13)
Loewner and Bézout matrices (1988) (13)
Moore-penrose involutions in the classes of laplacians and simplices (1995) (12)
A note on permanents and generalized complementary basic matrices (2012) (12)
Intertwining and testing matrices corresponding to a polynomial (1987) (12)
On a theorem of Everitt, Thompson, and de Pillis (1994) (11)
Generalized Hessenberg matrices (2004) (11)
Combined matrices in special classes of matrices (2011) (11)
Some results on the Bergstrom and Minkowski inequalities (1996) (11)
The rank of extreme positive operators on polyhedral cones (1978) (11)
Some Inequalities for the Spectrum of a Matrix (1960) (10)
Characterizations of MMA-matrices (1988) (10)
Additive compound graphs (1998) (10)
MATRICES AND GRAPHS IN EUCLIDEAN GEOMETRY (2005) (10)
DOUBLY STOCHASTIC MATRICES AND OPTIMIZATION (1988) (10)
A factorization of totally nonsingular matrices over a ring with identity (2000) (10)
Dense alternating sign matrices and extensions (2014) (9)
An estimate for the nonstochastic eigenvalues of doubly stochastic matrices (1995) (9)
An extremal problem for the spectral radius of a graph (1992) (9)
An observation on the Hadamard product of Hermitian matrices (1995) (9)
A minimax problem for graphs and its relation to generalized doubly stochastic matrices (1990) (9)
Ranks of dense alternating sign matrices and their sign patterns (2015) (8)
Generalized totally positive matrices (2000) (8)
Generalized totally nonnegative matrices (2002) (8)
Moore-Penrose biorthogonal systems in Euclidean spaces (2003) (8)
Subtotally positive and Monge matrices (2006) (7)
Estimates and iteration procedures for proper values of almost decomposable matrices (1964) (7)
Equilibrated anti-Monge matrices (2001) (7)
Isodynamic systems in Euclidean spaces and an $n$-dimensional analogue of a theorem by Pompeiu (1977) (7)
Geršgorin discs revisited (2013) (7)
Some inheritance properties for complementary basic matrices (2010) (7)
Recent advances in graph theory : proceedings of the Symposium held in Prague, June 1974 (1975) (7)
Geometry of the Laplacian (2005) (6)
Remarks on Monge matrices (2002) (6)
Some Estimates of the Proper Values of Matrices (1965) (6)
A note on sign-nonsingular matrices (2005) (6)
Irreducibility of compound matrices (1979) (5)
Inversion of e-simple block matrices☆ (2005) (5)
Old and new about positive definite matrices (2015) (5)
Generalized oscillatory matrices (2003) (5)
Diagonal blocks of two mutually inverse positive definite block matrices (1997) (5)
Some inverse problems for elliptic matrices with zero diagonal (2001) (4)
Some Applications of Matrices and Graphs in Euclidean Geometry (2006) (4)
Tropical tensor product and beyond (2018) (4)
A note on the row-rhomboidal form of a matrix (1996) (4)
A subclass of symmetric Loewner matrices (1992) (4)
Professor Vlastimil Pták died (2000) (4)
Polynomials compatible with a symmetric Loewner matrix (1993) (4)
Permanents, determinants, and generalized complementary basic matrices (2014) (4)
More on G-matrices (2013) (4)
Some graph theoretic properties of generalized complementary basic matrices (2013) (4)
Quasidirect Addition of Matrices and Generalized Inverses (1993) (3)
Minimal polynomial and the rank of principal submatrices of a matrix (1981) (3)
Some inequalities for the Hadamard product of matrices (1996) (3)
Some inverse problems for acyclic matrices (1997) (3)
A quantitative extension of the Perron-Frobenius theorem for doubly stochastic matrices (1975) (3)
Remarks on the Sherman-Morrison-Woodbury formulae (2003) (3)
Irreducibility of associated matrices (1981) (3)
Combinatorial aspects of generalized complementary basic matrices (2013) (3)
Block analogies of comparison matrices (1997) (3)
Minimal sets of vectors which generate $R_n$ with excess $k$ (1979) (3)
Suborthogonality and orthocentricity of matrices (2009) (3)
A remark on positive definite matrices (1960) (3)
Some inequalities related to M-matrices (1998) (2)
Mathematical Institute of the Academy--50 Years (2003) (2)
On a Special Class of Generalized Doubly Stochastic Matrices and Its Relation to Bézier Polygons (1995) (2)
List of publications of Vlastimil Pták, 1995–1999 (2000) (2)
Strong Majorization for Hermitian Matrices (1997) (2)
Two Isoperimetric Problems for Euclidean Simplices (2006) (2)
On qualitative angle properties of simplexes (1957) (2)
Some Connections between the Drazin Inverse, P-Matrices, and the Closure of Inverse M-Matrices (1990) (2)
On a conjecture of P. R. Vein and its generalization (1984) (2)
Majorization in Euclidean geometry and beyond (2015) (2)
Vlastimil Pták (8 November 1925 – 9 May 1999) (2000) (2)
On the range of the Hadamard product of a positive definite matrix and its inverse (1988) (2)
Someinverseproblemsforellipticmatriceswith zero diagonal (2001) (2)
Characterizations of Bézout and Hankel-Bézout matrices (1988) (2)
A note on nonnegative matrices (1977) (1)
Graphs and other combinatorial topics : proceedings of the third Czechoslovak Symposium on Graph Theory, held in Prague, August 24th to 27th, 1982 (1983) (1)
Some results on eigenvalues of nonnegative matrices (1974) (1)
Signed distance graphs (1969) (1)
A numerical approach to long cycles in graphs and digraphs (2001) (1)
Combinatorial properties of sign-patterns in some classes of matrices (1983) (1)
Two results on basic oscillatory matrices (2004) (1)
A deflation formula for tridiagonal matrices (1980) (1)
Remarks on eigenvalues of Hankel matrices (1991) (1)
Dominant matrices and max algebra (2011) (1)
Factorizable matrices (2013) (1)
Vladimír Doležal (22. 3. 1934–8. 1. 2002) (2002) (1)
Reminiscences related to graph theory (2007) (1)
Some results on combined matrices (2017) (1)
Norms and Their Use for Estimation of Eigenvalues (1986) (0)
Symmetric Matrices. Positive Definite and Semidefinite Matrices (1986) (0)
A note on strongly dense matrices (2015) (0)
Solution of a problem of Prof. E. Čech (1952) (0)
On the occasion of the 60th birthday of Jiří Sedláček (1984) (0)
Theory of Matrices. by Peter Lancaster. Academic Press, New York and London (1969). 316 pp. U.S. $11. (1970) (0)
The generalized Gräffe method and a modification of it (1963) (0)
A New Characterization of Generalized Complementary Basic Matrices (2014) (0)
A note on strongly dense matrices (2015) (0)
Basic Concepts of the Theory of Matrices (1986) (0)
Professor Bohdan Zelinka (May, 1940--February 5, 2005) (2007) (0)
M-Matrices (Matrices of Classes K and K0) (1986) (0)
Acta Universitatis Carolinae. Mathematica et Physica (1974) (0)
Graphs and Matrices (1986) (0)
DIMATIA surveys (related to the Fifth Czech and Slovak Symposium on Combinatorics, Graph Theory, Algorithms and Applications held in Prague on July 6-11, 1998) (2001) (0)
Matrices and Polynomials. Stable Matrices (1986) (0)
Direct Methods for Solving Linear Systems (1986) (0)
Max algebraic complementary basic matrices (2014) (0)
Ela Ultrametric Sets in Euclidean Point Spaces (1998) (0)
Numerical Methods for Computing Eigenvalues of Matrices (1986) (0)
lrreduclblllty of Associated Matrices (1981) (0)
Iterative Methods for Solving Linear Systems (1986) (0)
Further geometric objects (2011) (0)
Tensor Product of Matrices. Compound Matrices (1986) (0)
LOCALIZATION OF DOMINANT EIGENPAIRS AND PLANTED COMMUNITIES BY MEANS OF FROBENIUS INNER PRODUCTS DARIO FASINO AND FRANCESCO TUDISCO (2018) (0)
A matricial approach to Euclidean geometry (2011) (0)
Some observations on variance matrices (2013) (0)
Foreword (2001) (0)
Nonnegative Matrices. Stochastic and Doubly Stochastic Matrices (1986) (0)
Application of graphs to the Gaussian elimination method (1980) (0)
Hrátky s geometrií, čísly a maticemi (2010) (0)
Qualitative properties of the angles in a simplex (2011) (0)
Matrices and Graphs in Geometry: Simplex geometry (2011) (0)
A new look at totally positive matrices (2016) (0)
A numerical approach to longcycles in graphs and digraphs (2001) (0)
Numerical Solution of Algebraic and Transcendental Equations (1994) (0)
A new look at totally positive matrices (2016) (0)

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Other Resources About Miroslav Fiedler

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What Schools Are Affiliated With Miroslav Fiedler?

Miroslav Fiedler is affiliated with the following schools:

Charles University