Linear algebra

Linear algebra is the branch o mathematics concernin vector spaces, eften finite or coontably infinite dimensional, as well as linear cairtins 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 matrices an vectors.

The three-dimensional Euclidean space R³ is a vector space, an lines an planes passin through the origin are vector subspaces in R³.

Further reading

History

• Fearnley-Sander, Desmond, "Hermann Grassmann and the Creation of Linear Algebra", American Mathematical Monthly 86 (1979), pp. 809–817.
• Grassmann, Hermann (1844), 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, Leipzig: O. Wigand

Introduction

• Anton, Howard (2005), Elementary Linear Algebra (Applications Version) (9th ed.), Wiley International
• Banerjee, Sudipto; Roy, Anindya (2014), Linear Algebra and Matrix Analysis for Statistics, Texts in Statistical Science (1st ed.), Chapman and Hall/CRC, ISBN 978-1420095388
• Bretscher, Otto (2004), Linear Algebra with Applications (3rd ed.), Prentice Hall, ISBN 978-0-13-145334-0
• Farin, Gerald; Hansford, Dianne (2004), Practical Linear Algebra: A Geometry Toolbox, AK Peters, ISBN 978-1-56881-234-2
• Hefferon, Jim (2008), Linear Algebra
• Kolman, Bernard; Hill, David R. (2007), Elementary Linear Algebra with Applications (9th ed.), Prentice Hall, ISBN 978-0-13-229654-0
• Lay, David C. (2005), Linear Algebra and Its Applications (3rd ed.), Addison Wesley, ISBN 978-0-321-28713-7
• Leon, Steven J. (2006), Linear Algebra With Applications (7th ed.), Pearson Prentice Hall, ISBN 978-0-13-185785-8
• Murty, Katta G. (2014) Computational and Algorithmic Linear Algebra and n-Dimensional Geometry, World Scientific Publishing, ISBN 978-981-4366-62-5. Chapter 1: Systems of Simultaneous Linear Equations
• Poole, David (2010), Linear Algebra: A Modern Introduction (3rd ed.), Cengage – Brooks/Cole, ISBN 978-0-538-73545-2
• Ricardo, Henry (2010), A Modern Introduction To Linear Algebra (1st ed.), CRC Press, ISBN 978-1-4398-0040-9
• Sadun, Lorenzo (2008), Applied Linear Algebra: the decoupling principle (2nd ed.), AMS, ISBN 978-0-8218-4441-0
• Strang, Gilbert (2016), Introduction to Linear Algebra (5th ed.), Wellesley-Cambridge Press, ISBN 978-09802327-7-6

Advancit

• Axler, Sheldon (26 Februar 2004), Linear Algebra Done Right (2nd ed.), Springer, ISBN 978-0-387-98258-8
• Bhatia, Rajendra (15 November 1996), Matrix Analysis, Graduate Texts in Mathematics, Springer, ISBN 978-0-387-94846-1
• Demmel, James W. (1 August 1997), Applied Numerical Linear Algebra, SIAM, ISBN 978-0-89871-389-3
• Dym, Harry (2007), Linear Algebra in Action, AMS, ISBN 978-0-8218-3813-6
• Gantmacher, Felix R. (2005), Applications of the Theory of Matrices, Dover Publications, ISBN 978-0-486-44554-0
• Gantmacher, Felix R. (1990), Matrix Theory Vol. 1 (2nd ed.), American Mathematical Society, ISBN 978-0-8218-1376-8
• Gantmacher, Felix R. (2000), Matrix Theory Vol. 2 (2nd ed.), American Mathematical Society, ISBN 978-0-8218-2664-5
• Gelfand, Israel M. (1989), Lectures on Linear Algebra, Dover Publications, ISBN 978-0-486-66082-0
• Glazman, I. M.; Ljubic, Ju. I. (2006), Finite-Dimensional Linear Analysis, Dover Publications, ISBN 978-0-486-45332-3
• Golan, Johnathan S. (Januar 2007), The Linear Algebra a Beginning Graduate Student Ought to Know (2nd ed.), Springer, ISBN 978-1-4020-5494-5
• Golan, Johnathan S. (August 1995), Foundations of Linear Algebra, Kluwer, ISBN 0-7923-3614-3
• Golub, Gene H.; Van Loan, Charles F. (15 October 1996), Matrix Computations, Johns Hopkins Studies in Mathematical Sciences (3rd ed.), The Johns Hopkins University Press, ISBN 978-0-8018-5414-9
• Greub, Werner H. (16 October 1981), Linear Algebra, Graduate Texts in Mathematics (4th ed.), Springer, ISBN 978-0-8018-5414-9
• Hoffman, Kenneth; Kunze, Ray (1971), Linear algebra (2nd ed.), Englewood Cliffs, N.J.: Prentice-Hall, Inc., MR 0276251
• Halmos, Paul R. (20 August 1993), Finite-Dimensional Vector Spaces, Undergraduate Texts in Mathematics, Springer, ISBN 978-0-387-90093-3
• Friedberg, Stephen H.; Insel, Arnold J.; Spence, Lawrence E. (7 September 2018), Linear Algebra (5th ed.), Pearson, ISBN 978-0-13-486024-4
• Horn, Roger A.; Johnson, Charles R. (23 Februar 1990), Matrix Analysis, Cambridge University Press, ISBN 978-0-521-38632-6
• Horn, Roger A.; Johnson, Charles R. (24 Juin 1994), Topics in Matrix Analysis, Cambridge University Press, ISBN 978-0-521-46713-1
• Lang, Serge (9 Mairch 2004), Linear Algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, ISBN 978-0-387-96412-6
• Marcus, Marvin; Minc, Henryk (2010), A Survey of Matrix Theory and Matrix Inequalities, Dover Publications, ISBN 978-0-486-67102-4
• Meyer, Carl D. (15 Februar 2001), Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics (SIAM), ISBN 978-0-89871-454-8, archived frae the original on 31 October 2009
• Mirsky, L. (1990), An Introduction to Linear Algebra, Dover Publications, ISBN 978-0-486-66434-7
• Roman, Steven (22 Mairch 2005), Advanced Linear Algebra, Graduate Texts in Mathematics (2nd ed.), Springer, ISBN 978-0-387-24766-3
• Shafarevich, I. R.; Remizov, A. O (2012), Linear Algebra and Geometry, Springer, ISBN 978-3-642-30993-9
• Shilov, Georgi E. (1 Juin 1977), Linear algebra, Dover Publications, ISBN 978-0-486-63518-7
• Shores, Thomas S. (6 December 2006), Applied Linear Algebra and Matrix Analysis, Undergraduate Texts in Mathematics, Springer, ISBN 978-0-387-33194-2
• Smith, Larry (28 Mey 1998), Linear Algebra, Undergraduate Texts in Mathematics, Springer, ISBN 978-0-387-98455-1
• Trefethen, Lloyd N.; Bau, David (1997), Numerical Linear Algebra, SIAM, ISBN 978-0-898-71361-9

Guides

• Leduc, Steven A. (1 Mey 1996), Linear Algebra (Cliffs Quick Review), Cliffs Notes, ISBN 978-0-8220-5331-6
• Lipschutz, Seymour; Lipson, Marc (6 December 2000), Schaum's Outline of Linear Algebra (3rd ed.), McGraw-Hill, ISBN 978-0-07-136200-9
• Lipschutz, Seymour (1 Januar 1989), 3,000 Solved Problems in Linear Algebra, McGraw–Hill, ISBN 978-0-07-038023-3
• McMahon, David (28 October 2005), Linear Algebra Demystified, McGraw–Hill Professional, ISBN 978-0-07-146579-3
• Zhang, Fuzhen (7 Apryle 2009), Linear Algebra: Challenging Problems for Students, The Johns Hopkins University Press, ISBN 978-0-8018-9125-0

See also

• Matrix analysis
• Numerical linear algebra