List of linear algebra references

From Wikipedia, the free encyclopedia

This is a list of selected references for linear algebra, an important branch of mathematics.

Contents 1 Introductory linear algebra 1.1 Textbooks 1.2 Online books 1.3 Study guides and outlines 1.4 External links 2 Advanced linear algebra 2.1 Textbooks 3 Notes 4 See also

[edit] Introductory linear algebra

Introductory linear algebra refers to the material typically covered in a first or second-year course for scientists and engineers. The topics for such a course generally include:

• Systems of linear equations and row reduction
• Vectors and matrices
• Linear independence, linear subspaces, bases, and dimension
• Linear transformations, change of basis, and similarity
• Determinants
• Row space, column space, null space, and rank
• Introduction to vector spaces
• Eigenvalues and eigenvectors
• Orthogonality and inner product spaces
• Quadratic forms and symmetric matrices

[edit] Textbooks

Of these, the textbook by Lay had the highest sales rank (as of September 12, 2007) on Amazon.com, at #1,749. The next most popular were the books by Strang and by Poole, with sales rankings of #16,387 and #23,728. The textbook by Meyer has the widest coverage.

• Anton, Howard (December 27, 2004), Elementary Linear Algebra (9th ed.), Wiley, ISBN 978-0471669609 
• Bretscher, Otto (June 28, 2004), Linear Algebra with Applications (3rd ed.), Prentice Hall, ISBN 978-0131453340 
• Hansford, Dianne (December 15, 2004), Practical Linear Algebra: A Geometry Toolbox, AK Peters, ISBN 978-1568812342 
• Friedberg, Stephen H.; Insel, Arnold J. & Spence, Lawrence E. (November 11, 2002), Linear Algebra (4th ed.), Prentice Hall, ISBN 978-0130084514 
• Kolman, Bernard & Hill, David R. (May 3, 2007), Elementary Linear Algebra with Applications (9th ed.), Prentice Hall, ISBN 978-0132296540 
• Lay, David C. (August 22, 2005), Linear Algebra and Its Applications (3rd ed.), Addison Wesley, ISBN 978-0321287137 
• Leon, Steven J. (June 6, 2005), Linear Algebra with Applications (7th ed.), Prentice Hall, ISBN 978-0131857858 
• Meyer, Carl D. (February 15, 2001), Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics (SIAM), ISBN 978-0898714548 . Available online at http://www.matrixanalysis.com/DownloadChapters.html
• Poole, David (January 24, 2005), Linear Algebra: A Modern Introduction (2nd ed.), Brooks Cole, ISBN 978-0534998455 
• Strang, Gilbert (July 19, 2005), Linear Algebra and Its Applications (4th ed.), Brooks Cole, ISBN 978-0030105678 

[edit] Online books

• Beezer, Rob, A First Course in Linear Algebra
• Connell, Edwin H., Elements of Abstract and Linear Algebra
• Hefferon, Jim, Linear Algebra
• Matthews, Keith, Elementary Linear Algebra

[edit] Study guides and outlines

• Leduc, Steven A. (May 1, 1996), Linear Algebra (Cliffs Quick Review), Cliffs Notes, ISBN 978-0822053316 
• Lipschutz, Seymour & Lipson, Marc (December 6, 2000), Schaum's Outline of Linear Algebra (3rd ed.), McGraw-Hill, ISBN 978-0071362009 
• Lipschutz, Seymour (January 1, 1989), 3,000 Solved Problems in Linear Algebra, McGraw-Hill, ISBN 978-0070380233 
• McMahon, David (October 28, 2005), Linear Algebra Demystified, McGraw-Hill Professional, ISBN 978-0071465793 

[edit] External links

• MIT Linear Algebra Lectures by Gilbert Strang: free videos from MIT OpenCourseWare
• Streaming MIT Linear Algebra Lectures at Google Video
• Linear Algebra Toolkit.
• Linear Algebra on MathWorld.
• Linear Algebra overview and notation summary on PlanetMath.
• Matrix and Linear Algebra Terms on Earliest Known Uses of Some of the Words of Mathematics
• Linear Algebra by Elmer G. Wiens. Interactive web pages for vectors, matrices, linear equations, etc.
• Linear Algebra Solved Problems: Interactive forums for discussion of linear algebra problems, from the lowest up to the hardest level (Putnam).
• Linear Algebra for Informatics. José Figueroa-O'Farrill, University of Edinburgh
• Online Notes / Linear Algebra Paul Dawkins, Lamar University

[edit] Advanced linear algebra

Advanced linear algebra refers to the material typically covered in an upper-division undergraduate course directed at math majors, or in a graduate linear algebra course. The topics for such a course may include:

• Topics from introductory linear algebra
• Vector spaces and linear maps
• determinants, multilinear algebra, and tensors
• Linear functionals and the dual space
• Minimum and characteristic polynomials
• Jordan and rational canonical forms
• Matrix decompositions
• Orthogonal, unitary, symmetric, Hermitian, and normal matrices.
• Generalized inverses
• Numerical linear algebra and matrix analysis

[edit] Textbooks

• Axler, Sheldon (February 26, 2004), Linear Algebra Done Right (2nd ed.), Springer, ISBN 978-0387982588 
• Bhatia, Rajendra (November 15, 1996), Matrix Analysis, Graduate Texts in Mathematics, Springer, ISBN 978-0387948461 
• Demmel, James W. (August 1, 1997), Applied Numerical Linear Algebra, SIAM, ISBN 978-0898713893 
• Golan, Johnathan S. (January 2007), The Linear Algebra a Beginning Graduate Student Ought to Know (2nd ed.), Springer, ISBN 978-1402054945 
• Golub, Gene H. & Van Loan, Charles F. (October 15, 1996), Matrix Computations (3rd ed.), Johns Hopkins Studies in Mathematical Sciences, The Johns Hopkins University Press, ISBN 978-0801854149 
• Greub, Werner H. (October 16, 1981), Linear Algebra (4th ed.), Graduate Texts in Mathematics, Springer, ISBN 978-0801854149 
• Halmos, Paul R. (August 20, 1993), Finite-Dimensional Vector Spaces, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387900933 
• Horn, Roger A. & Johnson, Charles R. (February 23, 1990), Matrix Analysis, Cambridge University Press, ISBN 978-0521386326 
• Horn, Roger A. & Johnson, Charles R. (June 24, 1994), Topics in Matrix Analysis, Cambridge University Press, ISBN 978-0521467131 
• Lang, Serge (March 9, 2004), Linear Algebra (3rd ed.), Undergraduate Texts in Mathematics, Springer, ISBN 978-0387964126 
• Roman, Steven (March 22, 2005), Advanced Linear Algebra (2nd ed.), Graduate Texts in Mathematics, Springer, ISBN 978-0387247663 
• Shilov, Georgi E. (June 1, 1977), ISBN 978-0486635187 
• Shores, Thomas S. (December 6, 2006), Applied Linear Algebra and Matrix Analysis, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387331942 
• Smith, Larry (May 28, 1998), Linear Algebra, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387984551 

[edit] Notes

[edit] See also

• Linear algebra
• List of linear algebra topics