M-matrix

About: M-matrix is a research topic. Over the lifetime, 412 publications have been published within this topic receiving 15722 citations.

Nonnegative Matrices in the Mathematical Sciences

Abstract: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains 9. Input-output analysis in economics 10. The Linear complementarity problem 11. Supplement 1979-1993 References Index.

For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution

Abstract: We consider linear equations y = Φx where y is a given vector in ℝn and Φ is a given n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the following property holds: For every y having a representation y = Φx0by a coefficient vector x0 ∈ ℝmwith fewer than ρ · n nonzeros, the solution x1of the 1-minimization problem is unique and equal to x0. In contrast, heuristic attempts to sparsely solve such systems—greedy algorithms and thresholding—perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almost-spherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices. © 2006 Wiley Periodicals, Inc.

Handbook Of Linear Algebra

Abstract: Linear Algebra Linear Algebra Vectors, Matrices, and Systems of Linear Equations Jane Day Linear Independence, Span, and Bases Mark Mills Linear Transformations Francesco Barioli Determinants and Eigenvalues Luz M. DeAlba Inner Product Spaces, Orthogonal Projection, Least Squares, and Singular Value Decomposition Lixing Han and Michael Neumann Canonical Forms Leslie Hogben Other Canonical Forms Roger A. Horn and Vladimir V. Sergeichuk Unitary Similarity, Normal Matrices, and Spectral Theory Helene Shapiro Hermitian and Positive Definite Matrices Wayne Barrett Nonnegative and Stochastic Matrices Uriel G. Rothblum Partitioned Matrices Robert Reams Topics in Linear Algebra Schur Complements Roger A. Horn and Fuzhen Zhang Quadratic, Bilinear, and Sesquilinear Forms Raphael Loewy Multilinear Algebra J.A. Dias da Silva and Armando Machado Tensors and Hypermatrices Lek-Heng Lim Matrix Equalities and Inequalities Michael Tsatsomeros Functions of Matrices Nicholas J. Higham Matrix Polynomials Jorg Liesen and Christian Mehl Matrix Equations Beatrice Meini Invariant Subspaces G.W. Stewart Matrix Perturbation Theory Ren-Cang Li Special Types of Matrices Albrecht Bottcher and Ilya Spitkovsky Pseudospectra Mark Embree Singular Values and Singular Value Inequalities Roy Mathias Numerical Range Chi-Kwong Li Matrix Stability and Inertia Daniel Hershkowitz Generalized Inverses of Matrices Yimin Wei Inverse Eigenvalue Problems Alberto Borobia Totally Positive and Totally Nonnegative Matrices Shaun M. Fallat Linear Preserver Problems Peter Semrl Matrices over Finite Fields J. D. Botha Matrices over Integral Domains Shmuel Friedland Similarity of Families of Matrices Shmuel Friedland Representations of Quivers and Mixed Graphs Roger A. Horn and Vladimir V. Sergeichuk Max-Plus Algebra Marianne Akian, Ravindra Bapat, and Stephane Gaubert Matrices Leaving a Cone Invariant Bit-Shun Tam and Hans Schneider Spectral Sets Catalin Badea and Bernhard Beckermann Combinatorial Matrix Theory and Graphs Combinatorial Matrix Theory Combinatorial Matrix Theory Richard A. Brualdi Matrices and Graphs Willem H. Haemers Digraphs and Matrices Jeffrey L. Stuart Bipartite Graphs and Matrices Bryan L. Shader Sign Pattern Matrices Frank J. Hall and Zhongshan Li Topics in Combinatorial Matrix Theory Permanents Ian M. Wanless D-Optimal Matrices Michael G. Neubauer and William Watkins Tournaments T.S. Michael Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs Shaun M. Fallat and Leslie Hogben Spectral Graph Theory Steve Butler and Fan Chung Algebraic Connectivity Steve Kirkland Matrix Completion Problems Luz M. DeAlba, Leslie Hogben, and Amy Wangsness Wehe Numerical Methods Numerical Methods for Linear Systems Vector and Matrix Norms, Error Analysis, Efficiency, and Stability Ralph Byers and Biswa Nath Datta Matrix Factorizations and Direct Solution of Linear Systems Christopher Beattie Least Squares Solution of Linear Systems Per Christian Hansen and Hans Bruun Nielsen Sparse Matrix Methods Esmond G. Ng Iterative Solution Methods for Linear Systems Anne Greenbaum Numerical Methods for Eigenvalues Symmetric Matrix Eigenvalue Techniques Ivan Slapnicar Unsymmetric Matrix Eigenvalue Techniques David S. Watkins The Implicitly Restarted Arnoldi Method D.C. Sorensen Computation of the Singular Value Decomposition Alan Kaylor Cline and Inderjit S. Dhillon Computing Eigenvalues and Singular Values to High Relative Accuracy Zlatko Drmac Nonlinear Eigenvalue Problems Heinrich Voss Topics in Numerical Linear Algebra Fast Matrix Multiplication Dario A. Bini Fast Algorithms for Structured Matrix Computations Michael Stewart Structured Eigenvalue Problems | Structure-Preserving Algorithms, Structured Error Analysis Heike Fassbender Large-Scale Matrix Computations Roland W. Freund Linear Algebra in Other Disciplines Applications to Physical and Biological Sciences Linear Algebra and Mathematical Physics Lorenzo Sadun Linear Algebra in Biomolecular Modeling Zhijun Wu Linear Algebra in Mathematical Population Biology and Epidemiology Fred Brauer and Carlos Castillo-Chavez Applications to Optimization Linear Programming Leonid N. Vaserstein Semidefinite Programming Henry Wolkowicz Applications to Probability and Statistics Random Vectors and Linear Statistical Models Simo Puntanen and George P.H. Styan Multivariate Statistical Analysis Simo Puntanen, George A.F. Seber, and George P.H. Styan Markov Chains Beatrice Meini Applications to Computer Science Coding Theory Joachim Rosenthal and Paul Weiner Quantum Computation Zijian Diao Operator Quantum Error Correction Chi-Kwong Li, Yiu-Tung Poon, and Nung-Sing Sze Information Retrieval and Web Search Amy N. Langville and Carl D. Meyer Signal Processing Michael Stewart Applications to Analysis Differential Equations and Stability Volker Mehrmann and Tatjana Stykel Dynamical Systems and Linear Algebra Fritz Colonius and Wolfgang Kliemann Control Theory Peter Benner Fourier Analysis Kenneth Howell Applications to Geometry Geometry Mark Hunacek Some Applications of Matrices and Graphs in Euclidean Geometry Miroslav Fiedler Applications to Algebra Matrix Groups Peter J. Cameron Group Representations Randall R. Holmes and Tin-Yau Tam Nonassociative Algebras Murray R. Bremner, Lucia I. Murakami, and Ivan P. Shestakov Lie Algebras Robert Wilson Computational Software Interactive Software for Linear Algebra MATLAB Steven J. Leon Linear Algebra in Maple David J. Jeffrey and Robert M. Corless Mathematica Heikki Ruskeep'a'a Sage Robert A. Beezer, Robert Bradshaw, Jason Grout, and William Stein Packages of Subroutines for Linear Algebra BLAS Jack Dongarra, Victor Eijkhout, and Julien Langou LAPACK Zhaojun Bai, James Demmel, Jack Dongarra, Julien Langou, and Jenny Wang Use of ARPACK and EIGS D.C. Sorensen Summary of Software for Linear Algebra Freely Available on the Web Jack Dongarra, Victor Eijkhout, and Julien Langou Glossary Notation Index Index