Paper 3, Section I, C

Vector Calculus | Part IA, 2012

What does it mean for a second-rank tensor TijT_{i j} to be isotropic? Show that δij\delta_{i j} is isotropic. By considering rotations through π/2\pi / 2 about the coordinate axes, or otherwise, show that the most general isotropic second-rank tensor in R3\mathbb{R}^{3} has the form Tij=λδijT_{i j}=\lambda \delta_{i j}, for some scalar λ\lambda.

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