- #1
amitech
- 3
- 0
Homework Statement
e_j=g_(jk)e^k
where e_j is a covariant vector base
e^k is a a contravariant vector base
g_(jk) is the covariant metric
How to prove the following identity
- Thread starter amitech
- Start date
-
- Tags
- Identity
Click For Summary
Homework Help Overview
The discussion revolves around proving an identity involving covariant and contravariant vector bases, specifically the relationship expressed as e_j = g_(jk)e^k, where e_j represents a covariant vector base, e^k denotes a contravariant vector base, and g_(jk) is the covariant metric.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are exploring the definition of the covariant metric and questioning how to transition between covariant and contravariant vectors. There is a focus on understanding the nature of e_j and e^k as unit vectors rather than mere components.
Discussion Status
The discussion is currently examining foundational definitions and relationships between different types of vectors and metrics. Some participants are providing clarifications regarding the covariant metric and its implications for vector transformation, but no consensus or resolution has been reached yet.
Contextual Notes
There appears to be some ambiguity regarding the terms used, particularly the distinction between components and unit vectors in the context of the metric. Participants are also addressing the implications of using the metric to raise and lower indices.