See soorce fer Linear algebra

[[File:Linear subspaces with shading.svg|thumb|250px|right|The three-dimensional [[Euclidean space]] '''R'''<sup>3</sup> is a vector space, an lines an planes passin through the [[origin (mathematics)|origin]] are vector subspaces in '''R'''<sup>3</sup>.]]
'''Linear algebra''' is the branch o [[mathematics]] concernin [[vector space]]s, eften finite or [[coontably infinite]] dimensional, as well as [[linear cairt]]ins atween such spaces. Such an investigation is initially motivatit bi a [[seestem o linear equations]] containin several unkents. Such equations are naiturally represented uisin the formalism o [[Matrix (mathematics)|matrices]] an vectors.<ref>{{cite web|last=Weisstein|first=Eric|title=Linear Algebra|url=http://mathworld.wolfram.com/LinearAlgebra.html|work=From MathWorld--A Wolfram Web Resource.|publisher=Wolfram|accessdate=16 April 2012}}</ref>

==References==
{{Reflist}}
==Further reading==
===History===
* Fearnley-Sander, Desmond, "[https://www.jstor.org/stable/pdf/2320145.pdf?casa_token=OivQGvKhCREAAAAA:1DKkTImlBZdKc7f-9T5tb5gjNx_RBbC20OcrA_jM3_6ksW6Js7bs6qhvcCBjzBg3kD3Zq0Gr0mLe3w9HQiQIbLgv73HBTkYIj2HNlE_HyOh5fUJb7Nsy3A Hermann Grassmann and the Creation of Linear Algebra]", American Mathematical Monthly '''86''' (1979), pp.&nbsp;809–817.
* {{Citation|last=Grassmann|first= Hermann| title=Die lineale Ausdehnungslehre ein neuer Zweig der Mathematik: dargestellt und durch Anwendungen auf die übrigen Zweige der Mathematik, wie auch auf die Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erläutert|publisher= O. Wigand|location= Leipzig|year= 1844}}
===Introduction===
{{columns-list|colwidth=20em|
* {{Citation|last=Anton|first=Howard|year=2005|title=Elementary Linear Algebra (Applications Version)|publisher=Wiley International|edition=9th}}
* {{Citation | last = Banerjee | first = Sudipto | last2 = Roy | first2 = Anindya | date = 2014 | title = Linear Algebra and Matrix Analysis for Statistics | series = Texts in Statistical Science | publisher = Chapman and Hall/CRC | edition =  1st | isbn =  978-1420095388}}
* {{Citation|last=Bretscher|first=Otto|year=2004|title=Linear Algebra with Applications|publisher=Prentice Hall|edition=3rd|isbn=978-0-13-145334-0}}
* {{Citation|last=Farin|first=Gerald|last2=Hansford|first2=Dianne|
year=2004|title=Practical Linear Algebra: A Geometry Toolbox|publisher=AK Peters|isbn=978-1-56881-234-2}}
* {{Citation|last=Hefferon|first=Jim|year=2008|title=Linear Algebra|url=http://joshua.smcvt.edu/linearalgebra/|access-date=2020-05-29|archive-date=2014-03-01|archive-url=https://web.archive.org/web/20140301110706/http://joshua.smcvt.edu/linearalgebra/|url-status=dead}}
* {{Citation|last=Kolman|first=Bernard|last2=Hill|first2=David R.|year=2007|title=Elementary Linear Algebra with Applications|publisher=Prentice Hall|edition=9th|isbn=978-0-13-229654-0}}
* {{Citation|last=Lay|first=David C.|year=2005|title=Linear Algebra and Its Applications|publisher=Addison Wesley|edition=3rd|isbn=978-0-321-28713-7}}
* {{Citation|last=Leon|first=Steven J.|year=2006|title=Linear Algebra With Applications|publisher=Pearson Prentice Hall|edition=7th|isbn=978-0-13-185785-8|url-access=registration|url=https://archive.org/details/linearalgebrawit00leon}}
* Murty, Katta G. (2014) ''[http://www.worldscientific.com/worldscibooks/10.1142/8261 Computational and Algorithmic Linear Algebra and n-Dimensional Geometry]'', World Scientific Publishing, {{isbn|978-981-4366-62-5}}. ''[http://www.worldscientific.com/doi/suppl/10.1142/8261/suppl_file/8261_chap01.pdf Chapter 1: Systems of Simultaneous Linear Equations]''
* {{Citation|last=Poole|first=David|year=2010|title=Linear Algebra: A Modern Introduction|publisher=Cengage&nbsp;– Brooks/Cole|edition=3rd|isbn=978-0-538-73545-2}}
* {{Citation|last=Ricardo|first=Henry|year=2010|title=A Modern Introduction To Linear Algebra|publisher=CRC Press|edition=1st|isbn=978-1-4398-0040-9}}
* {{Citation|last=Sadun|first=Lorenzo|year=2008|title=Applied Linear Algebra: the decoupling principle|publisher=AMS|edition=2nd|isbn=978-0-8218-4441-0}}
* {{Citation|last=Strang|first=Gilbert|year=2016|title=Introduction to Linear Algebra|publisher=Wellesley-Cambridge Press|edition=5th|isbn=978-09802327-7-6}}
}}
===Advancit===
{{columns-list|colwidth=20em|
* {{Citation|last=Axler|first=Sheldon|date=February 26, 2004|title=Linear Algebra Done Right|publisher=Springer|edition=2nd|isbn=978-0-387-98258-8}}
* {{Citation|last=Bhatia|first=Rajendra|date=November 15, 1996|title=Matrix Analysis|series=Graduate Texts in Mathematics|publisher=Springer|isbn=978-0-387-94846-1}}
* {{Citation|last=Demmel|first=James W.|date=August 1, 1997|title=Applied Numerical Linear Algebra|publisher=SIAM|isbn=978-0-89871-389-3}}
* {{Citation|last=Dym|first=Harry|year=2007|title=Linear Algebra in Action|publisher=AMS|isbn=978-0-8218-3813-6}}
* {{Citation|last=Gantmacher|first=Felix R.|date=2005|title=Applications of the Theory of Matrices|publisher=Dover Publications|isbn=978-0-486-44554-0}}
* {{Citation|last=Gantmacher|first=Felix R.|year=1990|title=Matrix Theory Vol. 1|publisher=[[American Mathematical Society]]|edition=2nd|isbn=978-0-8218-1376-8}}
* {{Citation|last=Gantmacher|first=Felix R.|year=2000|title=Matrix Theory Vol. 2|publisher=American Mathematical Society|edition=2nd|isbn=978-0-8218-2664-5}}
* {{Citation|last=Gelfand|first=Israel M.|year=1989|title=Lectures on Linear Algebra|publisher=Dover Publications|isbn=978-0-486-66082-0}}
* {{Citation|last=Glazman|first=I. M.|last2=Ljubic|first2=Ju. I.|year=2006|title=Finite-Dimensional Linear Analysis|publisher=Dover Publications|isbn= 978-0-486-45332-3}}
* {{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=978-1-4020-5494-5}}
* {{Citation|last=Golan|first=Johnathan S.|date=August 1995|title=Foundations of Linear Algebra|publisher=Kluwer |isbn=0-7923-3614-3}}
* {{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=978-0-8018-5414-9}}
* {{Citation|last=Greub|first=Werner H.|date=October 16, 1981|title=Linear Algebra|series=Graduate Texts in Mathematics|publisher=Springer|edition=4th|isbn=978-0-8018-5414-9}}
* {{citation
 | last1 = Hoffman | first1 = Kenneth
 | last2 = Kunze | first2 = Ray | edition = 2nd
 | location = Englewood Cliffs, N.J.
 | mr = 0276251
 | publisher = Prentice-Hall, Inc.
 | title = Linear algebra
 | year = 1971}}
* {{Citation|last=Halmos|first=Paul R.|date=August 20, 1993|title=Finite-Dimensional Vector Spaces|series=Undergraduate Texts in Mathematics|publisher=Springer|isbn=978-0-387-90093-3}}
* {{Citation|last=Friedberg|first=Stephen H.|last2=Insel|first2=Arnold J.|last3=Spence|first3=Lawrence E.|date=September 7, 2018|volume=|pages=|title=Linear Algebra|publisher=Pearson|edition=5th|isbn=978-0-13-486024-4}}
* {{Citation|last=Horn|first=Roger A.|last2=Johnson|first2=Charles R.|date=February 23, 1990|title=Matrix Analysis|publisher=Cambridge University Press|isbn=978-0-521-38632-6}}
* {{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=978-0-521-46713-1}}
* {{Citation|last=Lang|first=Serge|date=March 9, 2004|title=Linear Algebra|series=Undergraduate Texts in Mathematics|edition=3rd|publisher=Springer|isbn=978-0-387-96412-6}}
* {{Citation|last1=Marcus|first1=Marvin|last2=Minc|first2=Henryk|year=2010|title=A Survey of Matrix Theory and Matrix Inequalities|publisher=Dover Publications|isbn=978-0-486-67102-4}}
* {{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=978-0-89871-454-8 |url=http://www.matrixanalysis.com/DownloadChapters.html |url-status=dead |archiveurl=https://web.archive.org/web/20091031193126/http://matrixanalysis.com/DownloadChapters.html |archivedate=October 31, 2009 }}
* {{Citation|last1=Mirsky|first1=L.|year=1990|title=An Introduction to Linear Algebra|publisher= Dover Publications|isbn=978-0-486-66434-7}}
* {{Citation|last=Roman|first=Steven|date=March 22, 2005|title=Advanced Linear Algebra|edition=2nd|series=Graduate Texts in Mathematics|publisher=Springer|isbn=978-0-387-24766-3}}
* {{Citation|last1=Shafarevich|first1 = I. R.|first2 = A. O|last2=Remizov|title = Linear Algebra and Geometry|publisher = Springer|year=2012|url = https://www.springer.com/mathematics/algebra/book/978-3-642-30993-9 |isbn = 978-3-642-30993-9}}
* {{Citation|last=Shilov|first=Georgi E.|date=June 1, 1977|publisher=Dover Publications|isbn=978-0-486-63518-7|title=Linear algebra}}
* {{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=978-0-387-33194-2}}
* {{Citation|last=Smith|first=Larry|date=May 28, 1998|title=Linear Algebra|series=Undergraduate Texts in Mathematics|publisher=Springer|isbn=978-0-387-98455-1}}
* {{Citation|last=Trefethen|first=Lloyd N.|last2=Bau|first2=David|date=1997|title=Numerical Linear Algebra|publisher=SIAM|isbn=978-0-898-71361-9}}
}}

===Guides===
* {{Citation|last=Leduc|first=Steven A.|date=May 1, 1996|title=Linear Algebra (Cliffs Quick Review)|publisher=Cliffs Notes|isbn=978-0-8220-5331-6}}
* {{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=978-0-07-136200-9}}
* {{Citation|last=Lipschutz|first=Seymour|date=January 1, 1989|title=3,000 Solved Problems in Linear Algebra|publisher=McGraw–Hill|isbn=978-0-07-038023-3}}
* {{Citation|last=McMahon|first=David|date=October 28, 2005|title=Linear Algebra Demystified|publisher=McGraw–Hill Professional|isbn=978-0-07-146579-3}}
* {{Citation|last=Zhang|first=Fuzhen|date=April 7, 2009|title=Linear Algebra: Challenging Problems for Students|publisher=The Johns Hopkins University Press|isbn=978-0-8018-9125-0}}

==See also==
* [[Matrix analysis]]
* [[Numerical linear algebra]]
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[[Category:Linear algebra| ]]
[[Category:Numerical analysis]]