Abstract
The chapter provides a unifying framework for the algebraic, geometric and analytic subjects. More precisely, the idea of structured sets (i.e., sets on which, or between which, functions or operations are defined) is developed. In particular, the chapter is of interest for the linear algebra, which will be studied in the next chapters. Complex numbers, the concepts of operation and vector space are introduced. Linear dependence and linear independence of vector systems is central for the sequel. Indeed, the proofs concerning finitely generated vector spaces, bases, vector subspaces, spanned subspaces, dimension and isomorphism are detailed and complete with examples and solved exercises.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Aitken, A.C.: Determinants and Matrices. Oliver and Boyd LTD, Edinburgh (1965)
Halmos, P.R.: Finite-Dimensional Vector Spaces. Springer, Heidelberg, New York (1974)
Lang, S.: Linear Algebra. Addison-Wesley Publishing Company, Reading, Mass (1966)
Lipschutz, S.: Theory and Problems of Linear Algebra. McGraw-Hill, New York (1968)
Pontryagin, L.S.: Foundations of Combinatorial Topology. Graylock Press, Rochester N.Y (1952)
Schwartz, J.T.: Introduction to Matrices and Vectors. Dover Publications, New York (1961)
Strang, G.: Linear Algebra and Its Applications. Academic Press, New York (1976)
Strang, G.: Introduction to Linear Algebra. Wellesley-Cambridge Press (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ventre, A.G.S. (2023). Vector Spaces. In: Calculus and Linear Algebra. Springer, Cham. https://doi.org/10.1007/978-3-031-20549-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-20549-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-20548-4
Online ISBN: 978-3-031-20549-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)