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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[f, dims]
SparseArray specify a tensor in a sparse positionvalue 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
Signature elements of 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
ArrayFlatten  ▪ Partition  ▪ PadLeft  ▪ PadRight
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