Abstract
The parallel connection of networks suggested the concept of parallel addition of matrices to Anderson and Duffin. The hybrid connection of networks also suggests a matrix opera¬tion. Using the Kirchhoff current and voltage equations, a new operation, hybrid addition, is defined for the set of Hermitian semidefinite matrices. This operation is an Hermitian semidefinite order preserving semigroup operation. Hybrid addition is closely related to the work of Anderson on "shorted operators", and to the gyration operation of linear programming and network synthesis