Three Problems on Vector and Tensor Fields

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• A set of quantities , whose inner product with an arbitrary vector is a tensor, then prove that the set of quantities is itself a tensor.

  . , mu_p and lower suffixes nu_1, nu_2, ... , nu_q r is a set of quantities whose inner product with an arbitrary vector v^r is equal to the tensor B with upper suffixes mu_1

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• 'Fundamentals of STATISTICAL AND THERMAL PHYSICS'

  On the right hand side you have g^{mu,rho}g_{rho,nu} If you let this act on a contravariant vector X^{nu} you get g^{mu,rho}g_{rho,nu} X^{nu} =g^{mu,rho} X_{rho} = X^{mu} I.e. you get the same vector back because you bring the index down and

• Vector transformation

  In this notation you denote the components of a tensor in a transformed coordinate system (S') by putting a prime on the index, instead of using a different name for the tensor itself. You also do this for the coordinates.

• Dipole Interactions

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• Integral of a Matrix Dot Product : Calculating Traction from Stress Tensor Matrix

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• Tensor Products of Su(2) Operators

  Part c) The Hamiltonian is: H = q_3 x I + I x q_2 Note that while q_3 and q_2 don't commute, the two terms do commute because now the q_3 and q_2 act on different spaces (i.e. they act on different components of the state vector).