Let M, M,..., Mn be a sequence of matrices. Each matrix M; has dimension ri-1 ....

  

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Let M, M,..., Mn be a sequence of matrices. Each matrix M; has dimension ri-1 . The minimum cost of multiplying matrices M X M X ...x Mn can be computed as follows. Let cij, i j, be the minimum cost of multiplying matrices M Mi+ ... Mj. Then we can show that Cij = 0 if j = i min {Cik+ Ck+1, +ri-1rkrj} if j> i. ik Let M, M,..., Mn be a sequence of matrices. Each matrix M; has dimension ri-1 . The minimum cost of multiplying matrices M X M X ...x Mn can be computed as follows. Let cij, i j, be the minimum cost of multiplying matrices M Mi+ ... Mj. Then we can show that Cij = 0 if j = i min {Cik+ Ck+1, +ri-1rkrj} if j> i. ik