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In the numerical analysis of physical problems, there often arise large matrices which exhibit certain kinds of block-symmetry when partitioned appropri- ately. In- this article, the structures of the frequently-occurring hyper-circulant and hyper-Jacobi matrices are examined, and it is shown how the calculation of any analytic function of such matrices may be reduced to the calculation of functions of the submatrices. Examples drawn from current engineering literature are given as well as small illustrative examples.- 1. Introduction. The coefficient matrices of many matrix equations (both algebraic and differential) which arise in engineering and chemistry may easily be partitioned into square submatrices of equal order. It is known that if the sub- matrices commute with each other, the solution of the given matrix equation can

Reduction of functions of some partitioned matrices