Français
1. Duality. Covariance and contravariance in a vector space
Consider a vector space E of dimension n over a field K.
Most commonly, K designates the body of reals, the body of rationals or the body of complexes.
1.1 Physicists' vectors. Contravariance
Let
The Ultimate Scientific and Technical Reference
A Comprehensive Knowledge Base, with over 1,200 authors and 100 scientific advisors
+ More than 10,000 articles and 1,000 how-to sheets, over 800 new or updated articles every year
From design to prototyping, right through to industrialization, the reference for securing the development of your industrial projects
This article is included in
Mathematics
This offer includes:
Knowledge Base
Updated and enriched with articles validated by our scientific committees
Services
A set of exclusive tools to complement the resources
Practical Path
Operational and didactic, to guarantee the acquisition of transversal skills
Doc & Quiz
Interactive articles with quizzes, for constructive reading
Ongoing reading
Duality. Covariance and contravariance in a vector space
Duality. Covariance and contravariance in a vector space
Tensors in finite dimension
References
The Ultimate Scientific and Technical Reference
A Comprehensive Knowledge Base, with over 1,200 authors and 100 scientific advisors
+ More than 10,000 articles and 1,000 how-to sheets, over 800 new or updated articles every year
From design to prototyping, right through to industrialization, the reference for securing the development of your industrial projects
