Question
Define covariant and cotravariant tensors of rank 2. Prove that transform covariantly, where gij are the components of the matrix tensor of rank 2 and vi the components of a contravariant vector.
Answer :
Word Count : 214
A covariant tensor of rank 2 is a tensor whose components transform according to the rule: [ A'*{ij} = \frac{\partial x^p}{\partial x'^i} \frac{\partial x^q}{\partial x'^j} A*{pq} ] under a change of coordinates (x^i \to x'^i). _________ ____ ____ __________ ______ _____.
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A covariant tensor of rank 2 is a tensor whose components transform according to the rule: [ A'*{ij} = \frac{\partial x^p}{\partial x'^i} \frac{\partial x^q}{\partial x'^j} A*{pq} ] under a change of coordinates (x^i \to x'^i). _________ ____ ____ __________ ______ _____.
_____ ___ _______ _______ ________ ___ _____ ___ __________ ________.
_____ ______ ________ __________ ________ ________.
_______ ___ ___ __________ ______ ___ ____ ____ _________ _____.
________ _______ ___ _________ ________.
_______ ______ _________ _____ _______ ________ ______ __________.
______ _____ _______ ____ _______.
_____ ____ ________ _____ ______ _________ _____ ___ _______ ______ ____ ____.
_______ _____ ___ _______ __________.
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____ ___ ___ _____ ______ ____.
______ __________ ______ ____ ________ ______ __________ _________ ________ _____.
__________ _________ ____ ______ ____ ___ ____ _____ _______ _________.
__________ ___ ___ _____ _________ _____.
_______ _____ ___ ____ ___ _____ __________ _________ _____ ____.
______ _______ ____ ____ ____ ___ __________ _______.
_________ _______ ____ _________ ___ ____ __________ ___ _____ ______.
_________ __________ _________ ____ ______ ___.
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