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Index Notation

  1. Aug 25, 2009 #1
    I have a general question about index notation.

    For an arbitrary quantity, a,

    "a" denotes a scalar quantity.
    "a_i" denotes a vector.
    "a_ij" denotes a 2nd-order tensor.

    So, if I have something like "a_i*e_ij*b_j"

    Would this be like multiplying an nx1 vector, an mxm matrix, and an Lx1 vector? It would not be a possible operation, but I'm wondering if that what it means when you multiply quantities like that.
  2. jcsd
  3. Aug 25, 2009 #2
    Indexing is usually used when you have components that are closely related, like entries in a matrix or sequence, but the indeces themselves do not imply any particular structure.

    [itex](x_i)[/itex] could refer to a vector, sequence, n-tuple, or just a list of disparate objects.

    Similarly [itex](a_{ij})[/itex] could be the entries of an m x n matrix or a doubly indexed sequence of sequences (commonly seen in diagonalizing proofs).

    Provided the products are defined, one could have all sorts of indeces running around in a product.

  4. Aug 25, 2009 #3
    You could be looking at Tensor notation:

    Last edited by a moderator: Apr 24, 2017
  5. Aug 25, 2009 #4
    That is known as the "Einstein summation convention" and should be denoting Cartesian Tensor Notation. Also if your subscripts are seperated by a comma, that implys differentiation.
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