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 |
[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
Wikibooks has a book on the topic of
- 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
