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Rank/order of tensor

  1. Sep 11, 2009 #1
    I am confused about the difference between the rank and order of a tensor.

    On p 71 of Mathematical Physics 2nd Ed (Kusse and Westwig, 2006 Wiley-VCH), the rank of a tensor is described as identifying the number of basis vectors of the tensor but in some other books, this seems to be described as the order of a tensor.

    Online, I saw both terms used as though they refer to different things, but I can't rely on that information because I saw it in Wikipedia. In Wikipedia, I also saw a statement that the dyadic product between vectors creates a tensor of rank one, but that is not what I read in the book mentioned above.

  2. jcsd
  3. Sep 11, 2009 #2


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    The phrase "rank of a tensor" generally just refers to how many and what type of indices it has. "rank of a matrix" usually means the dimension of it's range. They are two completely different usages of the word "rank". The second meaning is what the wikipedia entry is referring to.
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