This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Tensors
Mathematica's uniform representation of vectors and matrices as lists automatically extends to tensors of any rank, allowing Mathematica's powerful list manipulation functions immediately to be applied to tensors, both numerical and symbolic.
Table construct a tensor of any rank from an expression
Array construct a tensor from a function: Array
SparseArray specify a tensor in a sparse form

Dimensions the dimensions of a tensor
ArrayDepth the rank of a tensor
ArrayQ test whether an object is a tensor of a given rank

MatrixForm display a tensor of any rank

KroneckerDelta identity tensor
LeviCivitaTensor totally antisymmetric tensor
Band specify banded structure in a sparse array

Transpose transpose to rearrange indices in any way
Dot (.) dot product
Inner generalized inner product
Outer generalized outer product
Tr generalized trace

Flatten flatten out any sequence of levels
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