IGNOU MPH 1 2026 - Define covariant and cotravariant tensors of rank 2. Prove t

Question

Define covariant and cotravariant tensors of rank 2. Prove that $a_i = g_{ij}v^j$ transform covariantly, where g_ij are the components of the matrix tensor of rank 2 and vⁱ the components of a contravariant vector.

19 Jan 2026

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). Its indices are subscripts, and it “co-varies” with the basis

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