Cascade Addition and Subtraction of Matrices
William N. Anderson, Thomas D. Morley, George E. Trapp · SIAM Journal on Algebraic and Discrete Methods · 1986
The cascade connection of electrical n-port networks motivates the cascade sum of matrices. The electrical network situation pertains to Hermitian positive semidefinite matrices, while in this work the cascade addition operation is also considered for arbitrary matrices. Various properties of the cascade sum are presented, including conditions which guarantee the existence of the cascade sum and the associativity of the cascade sum. A related operation, the cascade difference, is also treated. The underlying structure of the cascade operations is developed using the theory of the shorted operator.