In §4.6 several tensor operations have been described. The numerical tensor calculus requires the practical realisation of these operations. In this chapter we describe the performance and arithmetical cost of the operations for the different formats. The discussed operations are the addition in
, evaluation of tensor entries in
, the scalar product and partial scalar product in
, the change of bases in
, general binary operations in
, Hadamard product in
, convolution of tensors in
, matrix-matrix multiplication in
, and matrix-vector multiplication in
is devoted to special functions applied to tensors. In the last
we comment on the operations required for the treatment of Hartree-Fock and Kohn-Sham applications in quantum chemistry.
In connection with the tensorisation discussed in Chap. 14, further operations and their cost will be discussed.