Handbook of linear algebra

I. 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

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

Functions of matrices / Nicholas J. Higham

Quadratic, bilinear and sesquilinear forms / Raphael Lowey

Multilinear algebra / J.A. Dias de Silva and Armando Machado

Matrix equalities and inequalities / Michael Tsatsomeros

Matrix perturbation theory / Ren-Cang Li

Pseudospectra / Mark Embree

Singular values and singular value inequalities / Roy Mathias

Numerical range / Chi-Kwong Li

Matrix stability and inertia / Daniel Hershkowitz

Inverse eigenvalue problems / Alberto Borobia

Totally positive and totally negative matrices / Shaun M. Fallat

Linear preserver problems / Peter Šemrl

Matrices over integral domains / Shmuel Friedland

Similarities of families of matrices / Shmuel Friedland

Max-plus algebra / Marianne Akian, Ravindra Bapat, Stéphane Gaubert

Matrices leaving a cone invariant / Bit-Shun Tam and Hans Schneider.

II. Combinatorial matrix theory and graphs

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

Permanents / Ian M. Wanless

D-optimal designs / Michael G. Neubauer and William Watkins

Sign pattern matrices / Frank J. Hall and Zhongshan Li

Multiplicity lists for the eigenvalues of symmetric matrices with a given graph / Charles R. Johnson, António Leal Duarte, and Carlos M. Saiago

Matrix completion problems / Leslie Hogben and Amy Wangsness

Algebraic connectivity / Steve Kirkland.

III. Numerical methods

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

Symmetric matrix eigenvalue techniques / Ivan Slapničar

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 Drmač

Fast matrix multiplication / Dario A. Bini

Structured matrix computations / Michael Ng

Large-scale matrix computations / Roland W. Freund.

IV. Applications

Linear programming / Leonid S. Vaserstein

Semidefinite programming / Henry Wolkowicz

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

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

Linear algebra and mathematical physics / Lorenzo Sadun

Linear algebra in biomolecular modeling / Zhijun Wu

Coding theory / Joachim Rosenthal and Paul Weiner

Quantum computation / Zijian Diao

Information retrieval and web search / Amy Langville and Carl Meyer

Signal processing / Michael Stewart

Geometry / Mark Hunacek

Some applications of matrices and graphs in Euclidean geometry / Miroslav Fiedler

Matrix groups / Peter J. Cameron

Group representations / Randall Holmes and T.Y. Tam

Nonassociative algebras / Murray R. Bremner, Lucia I. Muakami and Ivan P. Shestakov

Lie algebras / Robert Wilson.

V. Computational software

METLAB / Steven J. Leon

Linear algebra in Maple / David J. Jeffrey and Robert M. Corless

Mathematica / Heikki Ruskeepää

BLAS / Jack Dongarra, Victor Eijkhout, and Julien Langou

LAPACK / Zhaojun Bai

Use of ARPACK and EIGS / D.C. Sorensen.