Abstract
So far, we have been dealing with matrices having only real entries and vector spaces with real scalars. Also , in any system of linear (difference or differential) equations, we assumed that the coefficients of an equation are all real. However, for many applications of linear algebra, it is desirable to extend the scalars to complex numbers. For example, by allowing complex scalars, any polynomial of degree n (even with complex coefficients) has n complex roots counting multiplicity. (This is well known as the fundamental theorem of algebra). By applying it to a characteristic polynomial of a matrix, one can say that all the square matrices of order n will have n eigenvalues counting multiplicity.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kwak, J.H., Hong, S. (2004). Complex Vector Spaces. In: Linear Algebra. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8194-4_7
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8194-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4294-5
Online ISBN: 978-0-8176-8194-4
eBook Packages: Springer Book Archive