Abstract
Chapter 8 introduces another algebraic system, called vector spaces (linear spaces) interlinking both internal and external operations. In this chapter vector spaces and closely related fundamental concepts, such as linear independence, basis, dimension, linear transformation and its matrix representation, eigenvalue, inner product space, Hilbert space, quadratic form, Jordan canonical form etc., are studied. Such concepts form an integral part of linear algebra. Vector spaces have multi-faceted applications. Such spaces over finite fields play an important role in computer science, coding theory, design of experiments and combinatorics. Vector spaces over the infinite fields Q of rationals are important in number theory and design of experiments and vector spaces over C are essential for the study of eigenvalues. As the concept of a vector provides a geometric motivation, vector spaces facilitate the study of many areas of mathematics and integrate the abstract algebraic concepts with the geometric ideas.
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Adhikari, M.R., Adhikari, A. (2014). Vector Spaces. In: Basic Modern Algebra with Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1599-8_8
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DOI: https://doi.org/10.1007/978-81-322-1599-8_8
Publisher Name: Springer, New Delhi
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