Decomposition theorem andk-hyper connection expressions for generalk-order cofactors

Twok-hyperconnection expressions of a generalk-order cofactorY(_i,j) are presented for the indefinite parameter matrixY of a linear system by applying directed hypergraph theory, and based on it a decomposition theorem ofY(_i,j) is derived. By this theorem, the multi-level tearing and analysis can be carried out easily for any linear large system. This is a new multilevel topological analysis method. Using proposed method the scale of systems which can be topologically analysed by a computer will be enlarged.