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Operation to make an (m+n)th rank tensor of rank-m and rank-n tensors

  1. Jul 2, 2013 #1
    1. The problem statement, all variables and given/known data

    We know that c[ij] = ab[j] is a way to make a rank-2 tensor from two rank-1 tensors. We also know that C[abcxyz]=A[abc]B[xyz] is a way to make a rank-6 tensor from two rank-3 tensors. However, is there a matrix representation of this? I know the idea of a 6-dimensional matrix is painful and seemingly-unwieldy, but the question came up when I was writing myself some classical mechanics notes. The Levi-Civita symbol, if re-realized as a 3D "matrix", can be written as a 3D "matrix" whose "layers" are the three rotation matrices Rx, Ry, Rz, and feeding in the argument theta = Pi/2.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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