2. How it works

2.1. Single block representation

\[ \left[ \begin{array}{c} o_0 \\ o_1 \\ o_2 \\ \vdots \\o_n \end{array} \right]= \left[ \begin{array}{ccccc} s_{00} & s_{01} &s_{02} & \hdots & s_{0n} \\ s_{10} & s_{11} &s_{12} & \hdots & s_{1n} \\ s_{20} & s_{21} &s_{22} & \hdots & s_{2n} \\ \vdots & \vdots &\vdots & \ddots & \vdots \\ s_{n0} & s_{n1} &s_{n2} & \hdots & s_{nn} \\ \end{array} \right] \left[ \begin{array}{c} i_0 \\ i_1 \\ i_2 \\ \vdots \\i_n \end{array} \right] =S \left[ \begin{array}{c} i_0 \\ i_1 \\ i_2 \\ \vdots \\i_n \end{array} \right] \]

2.2. Recursion algorithm

\[ \begin{array}{ccc} S1[nxn] = \left[ \begin{array}{cc} S1_{00} & S1_{01} \\ S1_{10} & S1_{11} \\ \end{array} \right] & \quad & S1[mxm] = \left[ \begin{array}{cc} S1_{00} & S1_{01} \\ S1_{10} & S1_{11} \\ \end{array} \right] \\ \end{array} \]