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The best linear algebra books

2016-07-24

If you would follow the road to linear algebra here are some trustworthy signposts.

Generalist

These books develop the subject with minimal prerequisites. They cover a broad range of theory and selected applications.

• Axler, S. J. (2014). Linear algebra done right. New York: Springer-Verlag.
• Curtis, C. W. (1984). Linear algebra: An introductory approach. New York: Springer-Verlag.
• Greub, W. H. (1975). Linear algebra. New York: Springer-Verlag.
• Halmos, P. R. (1958). Finite-dimensional vector spaces. Princeton, N.J: Van Nostrand.
• Herstein, I. N., & Winter, D. J. (1988). A primer on linear algebra. New York: Macmillan.
• Hoffman, K., & Kunze, R. A. (1971). Linear algebra. Englewood Cliffs, N.J: Prentice-Hall.
• Katznelson, Y., & Katznelson, Y. R. (2008). A (terse) introduction to linear algebra. Providence, R.I: American Mathematical Society.
• Lax, P. D., & Lax, P. D. (2007). Linear algebra and its applications. Hoboken, N.J: Wiley-Interscience.

Historical

All mathematics is a work in progress and we should never take its current definitions as sacred. Learn the evolution of linear algebra and see how different formulations battled it out.

• Crowe, M. J. (1994). A history of vector analysis: The evolution of the idea of a vectorial system. Dover Pub.
• Grassmann, H. (1995). A new branch of mathematics: The “Ausdehnungslehre” of 1844 and other works. Chicago: Open Court.

Theoretical

These books develop the subject rigorously, often on generalized assumptions.

• Aluffi, P. (2009). Algebra: Chapter 0. Providence, R.I: American Mathematical Society.
• Blyth, T. S. (1990). Module theory: An approach to linear algebra. Oxford [England: Clarendon Press.
• Bourbaki, N. (1989). Algebra I. Berlin: Springer-Verlag.
• Brown, W. C. (1988). A second course in linear algebra. New York: Wiley.
• Curtis, M. L., & Place, P. (1990). Abstract linear algebra. New York: Springer-Verlag.
• Golan, J. S. (2012). The linear algebra a beginning graduate student ought to know. Dordrecht: Springer.
• Jacobson, N. (1951). Lectures in abstract algebra: Linear algebra. 2 eks. New York, Van Nostrand Reinhold.
• Lang, S. (1987). Linear algebra. New York: Springer-Verlag.
• Roman, S. (2008). Advanced linear algebra. New York: Springer.
• Shakarchi, R., & Lang, S. (1996). Solutions manual for Lang’s Linear algebra. New York: Springer.
• Valenza, R. J. (1993). Linear algebra: An introduction to abstract mathematics. New York: Springer-Verlag.
• Weintraub, S. H., & Mathematical Association of America. (2011). A guide to advanced linear algebra. Washington, DC: Mathematical Association of America.

Numerical

These describe matrix forms and efficient algorithms for getting numerical answers.

• Golub, G. H., & Van, L. C. F. (2013). Matrix computations.
• Herstein, I. N., & Winter, D. J. (1988). Matrix theory and linear algebra. New York: Macmillan.
• Horn, R. A., & Johnson, C. R. (2013). Matrix analysis, second edition. Cambridge: Cambridge University Press.
• Trefethen, L. N., & Bau, D. (1997). Numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics.

Practice, practice

While all math books provide exercises, these books are comprised entirely of them, along with hints and solutions.

• Blyth, T. S., & Robertson, E. F. (1984). Algebra through practice: A collection of problems in algebra, with solutions. Cambridge: Cambridge University Press.
• Halmos, P. R. (1995). Linear algebra problem book. Washington, DC: Mathematical Association of America.
• Lipschutz, S. (1988). Three thousand solved problems in linear algebra. New York: McGraw-Hill.
• Prasolov, V. V., & Ivanov, S. (1994). Problems and theorems in linear algebra. Providence, R.I: American Mathematical Society.
• Zhang, F. (1996). Linear algebra: Challenging problems for students. Baltimore: Johns Hopkins University Press.

Extended

Directions for further study.

• Greub, W. H. (1978). Multilinear algebra. New York: Springer-Verlag.
• Rudin, W. (1991). Functional analysis. New York: McGraw-Hill.
• Schaefer, H. H., & Wolff, M. P. (1999). Topological vector spaces. S.l.: Springer.
• Weinreich, G. (1998). Geometrical vectors. Chicago: University of Chicago Press.

Weird Russian

Supposedly using outdated notation but packed with wisdom.

• Akivis, M. A., Golʹdberg, V. V., & Silverman, R. A. (1977). An introduction to linear algebra and tensors. New York: Dover Publications.
• Gelʹfand, I. M. (1989). Lectures on linear algebra. New York: Dover Publications.
• Shilov, G. E. (1977). Linear algebra. New York: Dover Publications.

Written by Joe "begriffs" Nelson