The rational canonical form, or Frobenius normal form, of a square matrix is a block diagonal matrix which is similar to the matrix and where the blocks are companion matrices. The blocks are C(d₁),C(d₂),…, C(d_k), where d₁,d₂,…,d_k are monic polynomials such that d_i divides d_i+1 and C(d_i) denotes the companion matrix of d_i. The minimal polynomial equals d_k and the characteristic polynomial equals the product d₁d₂…d_k. See Jordan normal form, Structure theorem (for modules).