Abstract
The preceding chapters made heavy use of vectors in the plane and in space. The enormous utility of the concept of vectors has prompted mathematicians and physicists to generalize this concept to include other objects that at first glance have no resemblance whatsoever with the planar and spatial vectors. In this chapter, we shall study this generalization in its limited form, i. e., only in an algebraic context. Although the analysis of vectors is discussed in Chapter 8, it is confined to vectors in space. The analysis of generalized vectors is the subject of differential geometry and functional analysis that are beyond the scope of this book.1
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Additional Reading
Auer, J.W. Linear Algebra with Applications, Prentice-Hall, 1991 is an elementary and readable book that the reader may find useful.
Friedberg, S., Insel, A., and Spence, L. Linear Algebra, Prentice-Hall, 1997 is another elementary and readable book with many examples.
Axler, S. Linear Algebra Done Right, Springer-Verlag, 1996 is a little more advanced and formal, but very clear and readable.
Halmos, P. Finite Dimensional Vector Spaces, 2nd ed., Van Nostrand, 1958 is a classic, which the reader should return to after a little more sophistication.
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© 2000 Springer Science+Business Media New York
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Hassani, S. (2000). Vectors. In: Mathematical Methods. Undergraduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21562-4_4
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DOI: https://doi.org/10.1007/978-0-387-21562-4_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-0529-1
Online ISBN: 978-0-387-21562-4
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