Resources on Linear Algebra

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Resources on Linear Algebra

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 Bttcher, Introduction to Large Truncated Toeplitz Matrices
• Aleksandr Ivanovich Borisenko, Vector and Tensor Analysis with Applications
• Anita Schbel, 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 Ltkepohl, 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 Eldn, 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

• LAPACKLinear 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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