The horizontal decomposition in the Outside VMT algorithm, for the case where | I | > | J |. (a) AI, Jsustains the pre-condition (see Figure 12 for notations). (b) AI, Jis partitioned horizontally to and , where is computed recursively. (c) If μi, jis of the form ⊕q∈[0,i)(βq, i⊗ αq, j), then the pre-condition for computing is established, by updating to be (in this example L = I1, since I2 ends before J starts. The corresponding sub-matrix of β is not shown). In the case where μi, j= ⊕q∈(j,n](αi, q⊗ βj, q), the pre-condition is met without any need for performing a matrix multiplication. Then, is computed recursively (not shown).