Resources on Linear Algebra

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Below are list of useful (some of them are classical) resources and references to learn further about Linear Algebra.

Online Journal papers
Books on Linear Algebra
Software / Programming
Video
Other Online Resources
Journals

Online Journal papers

• Louis Guttman, Enlargement Methods for Computing the Inverse Matrix, The Annals of Mathematical Statistics. Volume 17, Number 3 (1946), 336-343.
• Frederick V. Waugh, Paul S. Dwyer, Compact Computation of the Inverse of a Matrix, The Annals of Mathematical Statistics. Volume 16, Number 3 (1945), 259-271. 

Books on Linear Algebra

• Arch W. Naylor, Linear Operator Theory in Engineering and Science
• Alan J. Laub, Matrix Analysis for Scientists and Engineers
• Alan Tucker, Linear Algebra: An Introduction to the Theory and Use of Vectors and Matrices
• Albrecht Böttcher, Introduction to Large Truncated Toeplitz Matrices
• Aleksandr Ivanovich Borisenko, Vector and Tensor Analysis with Applications
• Anita Schöbel, Locating Lines and Hyperplanes: Theory and Algorithms
• Ann E. Hirst, Vectors in Two or Three Dimensions
• Beresford N. Parlett, The Symmetric Eigenvalue Problem
• Bernard Kolman, Introductory Linear Algebra: An Applied First Course
• Bruce Cooperstein, Advanced Linear Algebra
• C. Sydney Burrus, Basic Vector Space Methods in Signal and Systems Theory
• Carl D. Meyer, Matrix Analysis and Applied Linear Algebra
• Charles R. Johnson, Matrix Analysis
• Charles F. Van Loan and Thomas F. Coleman, Handbook for Matrix Computations
• Daniel Alpay, The State Space Method: Generalizations and Applications
• David A. Harville, Matrix Algebra From a Statistician's Perspective
• David B. Damiano, A Course in Linear Algebra
• David C. Lay, Linear Algebra and Its Applications
• David Poole, Linear Algebra: A Modern Introduction
• David S. Watkins, Fundamentals of Matrix Computations
• Dennis S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas
• Eugenius Kaszkurewicz, Matrix Diagonal Stability in Systems and Computation
• Eric Carlen, Linear Algebra: From the Beginning. For Scientist and Engineers
• Gareth Williams, Linear Algebra with Applications
• Gene H. Golub & Van Loan, Matrix Computations
• George A. F. Seber, A Matrix Handbook for Statisticians
• George W. Hart, Multidimensional Analysis: Algebras and Systems for Science and Engineering
• Georgi E. Shilov, Linear Algebra (see also here)
• Gerald E. Farin, Practical Linear Algebra: A Geometry Toolbox
• Gernot Akemann, The Oxford Handbook of Random Matrix Theory
• Gilbert Strang, Introduction to Linear Algebra
• Greg W. Anderson, An Introduction to Random Matrices
• H. Ted Davis, Linear Algebra and Linear Operators in Engineering
• Helmut Lütkepohl, Handbook of Matrices
• Howard Anton, Elementary Linear Algebra with Applications
• Hugh G. Campbell, An Introduction to Matrices, Vectors, and Linear Programming
• Ilse C. F. Ipsen, Numerical Matrix Analysis: Linear Systems and Least Squares
• J. H. Wilkinson, The Algebraic Eigenvalue Problem
• J. S. R. Chisholm, Vectors in Three-Dimensional Space
• James E. Gentle, Matrix Algebra: Theory, Computations, and Applications in Statistics
• James W. Demmel, Applied Numerical Linear Algebra
• Jimmie Gilbert and Linda Gilbert, Linear Algebra and Matrix Theory
• Joan Robinson Westlake, Handbook of Numerical Matrix Inversion and Solution of Linear Equations
• John H. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms
• Kenneth Hoffman, Linear Algebra
• Larry E. Knop, Linear Algebra: A First Course with Applications
• Lars Eldén, Matrix Methods in Data Mining and Pattern Recognition
• Lloyd N. Trefethen, Numerical Linear Algebra
• Lloyd N. Trefethen, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
• Ludwik Silberstein, Elements of Vector Algebra
• Ludwik Silberstein, Projective Vector Algebra: An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels
• Mark S. Gockenbach, Finite-Dimensional Linear Algebra
• Mary Jane Sterling, Linear Algebra For Dummies
• Melvin Hausner, A Vector Space Approach to Geometry
• Murray R. Spiegel, Schaum's Outlines Vector Analysis
• Nicholas J. Higham, Functions of Matrices: Theory and Computation
• Paul R. Halmos, Finite-Dimensional Vector Spaces
• Raf Vandebril, Matrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods
• Rajendra Bhatia, Positive Definite Matrices
• Rao and Mitra, Generalized Inverse and Its application
• Ray M. Bowen, Introduction to Vectors and Tensors
• Richard A. Brualdi, A Combinatorial Approach to Matrix Theory and Its Applications
• Richard Bronson, Matrix Methods: Applied Linear Algebra
• Robert C. Wrede, Introduction to Vector and Tensor Analysis
• Roger Hart, The Chinese Roots of Linear Algebra
• Ron Larson, Elementary Linear Algebra
• Serge A. Lang, Linear Algebra
• Seymour Lipschutz, Schaum's Outline of Beginning Linear Algebra
• Seymour Lipschutz, Schaum's Outline of Linear Algebra Nice for practice
• Shayle Searle, Matrix Algebra Useful for Statistics
• Sheldon Jay Axler, Linear Algebra Done Right
• Stephen H. Friedberg, Linear Algebra
• Steven J. Leon, Linear Algebra with Applications
• Steven Roman, Advanced Linear Algebra
• T. P. Humphreys, A Reference Guide to Vector Algebra
• T. Proctor Hall, A geometrical vector algebra
• Thomas S. Shores, Applied Linear Algebra and Matrix Analysis
• Y. Saad, Iterative Methods for Sparse Linear Systems

Software / Programming

• LAPACK—Linear Algebra PACKage (see note from Jochen Voss)
• BLAS (Basic Linear Algebra Subprograms)
• Sage
• Maxima
• Linear Algebra software (for windows)
• Linear Algebra Toolkit
• GSL
• Matlab (commercial)

Video

• Gilbert Strang, MIT Course on Linear Algebra (also in YouTube)
• Khan academy, Linear Algebra's video

Online Resources

• Lecture Notes by Keith Matthews on Elementary Linear Algebra
• Rob Beezer's, A First Course in Linear Algebra
• David A. Santos, Linear Algebra Notes
• Jim Hefferon, Linear Algebra Text
• Paul's Online Linear Algebra Notes
• T. A. Carter, R. A. Tapia, A. Papakonstantinou, Linear Algebra- An Introduction to Linear Algebra for Pre-Calculus Students
• SOS Math Matrix Algebra

Journals

• Linear Algebra and its application (Elsevier)
• SIAM Journal on Matrix Analysis and Applications (SIMAX)

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