Abstract Indices and Tensor Spaces
A general homogeneous tensor is an element of a tensor product of copies of V and V*, such as
Label each factor in this tensor product with a Latin letter in a raised position for each contravariant V factor, and in a lowered position for each covariant V* position. In this way, write the product as
or, simply
It is important to remember that these last two expressions signify precisely the same object as the first. We shall denote tensors of this type by the same sort of notation, for instance
Read more about this topic: Abstract Index Notation
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