A one-form versus a dual basis vector

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SUMMARY

A one-form is not the same as a dual basis vector, although they are related concepts in linear algebra. Dual basis vectors are specific instances of one-forms, but not all one-forms qualify as dual basis vectors. The relationship can be understood as dual basis vectors corresponding to one-forms in the same way that basis vectors correspond to vectors.

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Scott4775
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Hi everyone,

Pardon the neophyte question, but is a one-form the same thing as a dual basis vector? If not, are they related in some way, or completely different concepts/entities?

Thank you!
 
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Welcome to PF.

The dual basis vectors are 1-forms, but not all 1-forms are dual basis vectors. In fact given a set of dual basis vectors we can construct any number of 1-forms.
 
Dual basis vectors are to one-forms as basis vectors are to vectors.
 

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