Mode-k flattening
In multilinear algebra, mode-m flattening, also known as matrixizing, matricizing is an operation that reshapes a multi-way array into a matrix denoted by .
Matrixizing may be regarded as a generalization of the mathematical concept of vectorizing.
Definition
The mode-m matrixizing of tensor is defined as the matrix. As the parenthetical ordering indicates, the mode-m column vectors are arranged by sweeping all the other mode indices through their ranges, with smaller mode indexes varying more rapidly than larger ones; thuswhere and
By comparison, the matrix that results from an unfolding has columns that are the result of sweeping through all the modes in a circular manner beginning with mode as seen in the parenthetical ordering. This is an inefficient way to matrixize.