Abstract
In this chapter we will prove the inverse and implicit mapping theorems, which have far-reaching applications. We will begin with the inverse mapping theorem and then derive the implicit mapping theorem from it.
Keywords
- Inverse Function Theorem
- Normed Vector Space
- Bijective Continuous Linear Mappings
- Rank Theorem
- Constrained Extremum
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 subscriptionsReferences
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms, 2nd edn. Springer-Verlag, Berlin (1997)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Coleman, R. (2012). The Inverse and Implicit Mapping Theorems. In: Calculus on Normed Vector Spaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3894-6_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-3894-6_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3893-9
Online ISBN: 978-1-4614-3894-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)