Vector Spaces

Mahima Ranjan Adhikari and Avishek Adhikari
Additional contact information
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)
Avishek Adhikari: University of Calcutta, Department of Pure Mathematics

Chapter Chapter 8 in Basic Modern Algebra with Applications, 2014, pp 273-354 from Springer

Abstract: 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.

Keywords: Abstract Vector Space; Jordan Normal Form; Linear Independence; Segre Characteristic; Rational Canonical Form (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1599-8_8

Ordering information: This item can be ordered from
http://www.springer.com/9788132215998

DOI: 10.1007/978-81-322-1599-8_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().