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Definition of a tensor

  1. Apr 6, 2013 #1
    I was reading this page: http://en.wikipedia.org/wiki/Tensor
    which said the definition of a tensor was a relation between two vectors. I then went down to the examples section and it had some sort of (n,m) notation. I had some theories on what they meant but none of them made sense. What do n and m represent?
  2. jcsd
  3. Apr 6, 2013 #2


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    ##n## is just the number of products of ##V^{*}## and ##m## is the number of products of ##V## which comprise the domain of the map; the codomain is just the reals.
  4. Apr 7, 2013 #3
    That is hardly true, a tensor is a linear object which maps n vectors and m one-forms into real numbers, and transforms in a coordinate invariant manner.
    That is like saying multiplication is defined as a relation between two numbers.
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