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


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

  • Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …   Wikipedia

  • Numerical linear algebra — is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing,… …   Wikipedia

  • List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

  • List of Jewish mathematicians — is a list that includes mathematicians who are or were verifiably Jewish or of Jewish descent. A G * Abraham Manie Adelstein [article in Oxford Dictionary of National Biography] , statistician * Hertha Ayrton [article in Oxford Dictionary of… …   Wikipedia

  • Linear map — In mathematics, a linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar… …   Wikipedia

  • Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… …   Wikipedia

  • List of academic disciplines — An academic discipline, or field of study, is a branch of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part), and recognized by the academic journals in which research is published, and… …   Wikipedia

  • List of Russian people — The Millennium of Russia monument in Veliky Novgorod, featuring the statues and reliefs of the most celebrated people in the first 1000 years of Russian history …   Wikipedia

  • List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”