List of linear algebra references

List of linear algebra references

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

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

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.
* Citation
last = Anton
first = Howard
date = December 27, 2004
title = Elementary Linear Algebra
publisher = Wiley
edition = 9th
isbn = 978-0471669609
* Citation
last = Bretscher
first = Otto
date = June 28, 2004
title = Linear Algebra with Applications
publisher = Prentice Hall
edition = 3rd
isbn = 978-0131453340
* Citation
last = Farin
first = Gerald
last = Hansford
first = Dianne
date = December 15, 2004
title = Practical Linear Algebra: A Geometry Toolbox
publisher = AK Peters
isbn = 978-1568812342
* Citation
last = Friedberg
first = Stephen H.
last2 = Insel
first2 = Arnold J.
last3 = Spence
first3 = Lawrence E.
date = November 11, 2002
title = Linear Algebra
publisher = Prentice Hall
edition = 4th
isbn = 978-0130084514
* Citation
last = Kolman
first = Bernard
last2 = Hill
first2 = David R.
date = May 3, 2007
title = Elementary Linear Algebra with Applications
publisher = Prentice Hall
edition = 9th
isbn = 978-0132296540
* Citation
last = Lay
first = David C.
date = August 22, 2005
title = Linear Algebra and Its Applications
publisher = Addison Wesley
edition = 3rd
isbn = 978-0321287137
* Citation
last = Leon
first = Steven J.
date = June 6, 2005
title = Linear Algebra with Applications
publisher = Prentice Hall
edition = 7th
isbn = 978-0131857858
* Citation
last = Meyer
first = Carl D.
date = February 15, 2001
title = Matrix Analysis and Applied Linear Algebra
publisher = Society for Industrial and Applied Mathematics (SIAM)
isbn = 978-0898714548. Available online at http://www.matrixanalysis.com/DownloadChapters.html
* Citation
last = Poole
first = David
date = January 24, 2005
title = Linear Algebra: A Modern Introduction
publisher = Brooks Cole
edition = 2nd
isbn = 978-0534998455
* Citation
last = Strang
first = Gilbert
date = July 19, 2005
title = Linear Algebra and Its Applications
publisher = Brooks Cole
edition = 4th
isbn = 978-0030105678

Online books

*Beezer, Rob, [http://linear.ups.edu/index.html "A First Course in Linear Algebra"]
*Connell, Edwin H., " [http://www.math.miami.edu/~ec/book/ Elements of Abstract and Linear Algebra] "
*Hefferon, Jim, " [http://joshua.smcvt.edu/linalg.html/ Linear Algebra] "
*Matthews, Keith, " [http://www.numbertheory.org/book/ Elementary Linear Algebra] "

tudy guides and outlines

* Citation
last = Leduc
first = Steven A.
date = May 1, 1996
title = Linear Algebra (Cliffs Quick Review)
publisher = Cliffs Notes
isbn = 978-0822053316
* Citation
last = Lipschutz
first = Seymour
last2 = Lipson
first2 = Marc
date = December 6, 2000
title = Schaum's Outline of Linear Algebra
publisher = McGraw-Hill
edition = 3rd
isbn = 978-0071362009
* Citation
last = Lipschutz
first = Seymour
date = January 1, 1989
title = 3,000 Solved Problems in Linear Algebra
publisher = McGraw-Hill
isbn = 978-0070380233
* Citation
last = McMahon
first = David
date = October 28, 2005
title = Linear Algebra Demystified
publisher = McGraw-Hill Professional
isbn = 978-0071465793

External links

* [http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm MIT Linear Algebra Lectures] by Gilbert Strang: free videos from MIT OpenCourseWare
* [http://video.google.com/videoplay?docid=7126729640834569444 Streaming MIT Linear Algebra Lectures] at Google Video
* [http://www.math.odu.edu/~bogacki/lat/ Linear Algebra Toolkit] .
* [http://mathworld.wolfram.com/topics/LinearAlgebra.html Linear Algebra] on MathWorld.
* [http://planetmath.org/encyclopedia/LinearAlgebra.html Linear Algebra overview] and [http://planetmath.org/encyclopedia/NotationInLinearAlgebra.html notation summary] on PlanetMath.
* [http://www.economics.soton.ac.uk/staff/aldrich/matrices.htm Matrix and Linear Algebra Terms] on [http://members.aol.com/jeff570/mathword.html Earliest Known Uses of Some of the Words of Mathematics]
* [http://www.egwald.ca/linearalgebra/index.php Linear Algebra] by Elmer G. Wiens. Interactive web pages for vectors, matrices, linear equations, etc.
* [http://www.mathlinks.ro/Forum/index.php?f=346 Linear Algebra Solved Problems] : Interactive forums for discussion of linear algebra problems, from the lowest up to the hardest level ("Putnam").
* [http://xmlearning.maths.ed.ac.uk Linear Algebra for Informatics] . José Figueroa-O'Farrill, University of Edinburgh
* [http://tutorial.math.lamar.edu/classes/linalg/linalg.aspx Online Notes / Linear Algebra] Paul Dawkins, Lamar University

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

Textbooks

* Citation
last = Axler
first = Sheldon
date = February 26, 2004
title = Linear Algebra Done Right
publisher = Springer
edition = 2nd
isbn = 978-0387982588
* Citation
last = Bhatia
first = Rajendra
date = November 15, 1996
title = Matrix Analysis
series = Graduate Texts in Mathematics
publisher = Springer
isbn = 978-0387948461
* Citation
last = Demmel
first = James W.
date = August 1, 1997
title = Applied Numerical Linear Algebra
publisher = SIAM
isbn = 978-0898713893
* Citation
last = Golan
first = Johnathan S.
date = January 2007
title = The Linear Algebra a Beginning Graduate Student Ought to Know
publisher = Springer
edition = 2nd
isbn = 978-1402054945
* Citation
last = Golub
first = Gene H.
last2 = Van Loan
first2 = Charles F.
date = October 15, 1996
title = Matrix Computations
series = Johns Hopkins Studies in Mathematical Sciences
publisher = The Johns Hopkins University Press
edition = 3rd
isbn = 978-0801854149
* Citation
last = Greub
first = Werner H.
date = October 16, 1981
title = Linear Algebra
series = Graduate Texts in Mathematics
publisher = Springer
edition = 4th
isbn = 978-0801854149
* Citation
last = Halmos
first = Paul R.
date = August 20, 1993
title = Finite-Dimensional Vector Spaces
series = Undergraduate Texts in Mathematics
publisher = Springer
isbn = 978-0387900933
* Citation
last = Horn
first = Roger A.
last2 = Johnson
first2 = Charles R.
date = February 23, 1990
title = Matrix Analysis
publisher = Cambridge University Press
isbn = 978-0521386326
* Citation
last1=Horn
first1=Roger A.
last2=Johnson
first2=Charles R.
date=June 24, 1994
title=Topics in Matrix Analysis
publisher=Cambridge University Press
isbn=978-0521467131
* Citation
last = Lang
first = Serge
date = March 9, 2004
title = Linear Algebra
series = Undergraduate Texts in Mathematics
edition = 3rd
publisher = Springer
isbn = 978-0387964126
* Citation
last = Roman
first = Steven
date = March 22, 2005
title = Advanced Linear Algebra
edition = 2nd
series = Graduate Texts in Mathematics
publisher = Springer
isbn = 978-0387247663
* Citation
last = Shilov
first = Georgi E.
date = June 1, 1977
publisher = Dover Publications
isbn = 978-0486635187
* Citation
last = Shores
first = Thomas S.
date = December 6, 2006
title = Applied Linear Algebra and Matrix Analysis
series = Undergraduate Texts in Mathematics
publisher = Springer
isbn = 978-0387331942
* Citation
last = Smith
first = Larry
date = May 28, 1998
title = Linear Algebra
series = Undergraduate Texts in Mathematics
publisher = Springer
isbn = 978-0387984551

Notes

ee also

* Linear algebra
* List of linear algebra topics


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