Mode-m flattening

In multilinear algebra, mode-m flattening[1] (also matrixizing, matricizing, or unfolding) is an operation that reshapes a tensor (a multi-way array) ${\mathcal {A}}$ into a matrix denoted by $A_{[m]}$ (a two-way array).

Matrixizing may be regarded as a generalization of the mathematical concept of vectorization.

Applications

This operation is used widely in Parafac and HOSVD.

References

Eldén, L.; Savas, B. (2009-01-01). "A Newton–Grassmann Method for Computing the Best Multilinear Rank-$(r_1,$ $r_2,$ $r_3)$ Approximation of a Tensor". SIAM Journal on Matrix Analysis and Applications. 31 (2): 248–271. CiteSeerX 10.1.1.151.8143. doi:10.1137/070688316. ISSN 0895-4798.

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[1] Eldén, L.; Savas, B. (2009-01-01). "A Newton–Grassmann Method for Computing the Best Multilinear Rank-$(r_1,$ $r_2,$ $r_3)$ Approximation of a Tensor". SIAM Journal on Matrix Analysis and Applications. 31 (2): 248–271. CiteSeerX 10.1.1.151.8143. doi:10.1137/070688316. ISSN 0895-4798.