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.
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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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.
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