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"can SparseArray take sparse arrays as elements?" simple answer no. You can make a single SparseArray of whatever depth you want though, eg for your example: SparseArray[{{k_, k_, i_, i_} -> 1, {k_, k_, i_, j_} /; (Abs[j - i] == 1 ) -> 1/4, {i_, j_, k_, k_} /; (Abs[j - i] == 1 ) -> 1/4 , {i_, j_, k_, l_} /; ...



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