Abstract
In this chapter we study different classes of maps between one or two K-vector spaces and the one dimensional K-vector space defined by the field K itself. These maps play an important role in many areas of Mathematics, including Analysis, Functional Analysis and the solution of differential equations. They will also be essential for the further developments in this book: Using bilinear and sesquilinear forms, which are introduced in this chapter, we will define and study Euclidean and unitary vector spaces in Chap. 12. Linear forms and dual spaces will be used in the existence proof of the Jordan canonical form in Chap. 16.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Charles Hermite (1822–1901).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Liesen, J., Mehrmann, V. (2015). Linear Forms and Bilinear Forms. In: Linear Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-24346-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-24346-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24344-3
Online ISBN: 978-3-319-24346-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)