RESUMO
Parallel subtraction is an operation defined on pairs of positive operators. In terms of electrical networks, one may pose the following problem: Given an electrical network, represented by a specified positive operator, determine the set of positive operators which when connected in parallel with the specified operator yield another prescribed operator. The set of solutions of this electrical network problem is shown to have a minimum. The minimum is termed "the parallel difference of the fixed operators," and the operation is termed "parallel subtraction." The parallel difference is used to obtain explicit error estimates for an iteration procedure which approximates the geometric mean of positive operators. This concept of the geometric mean reduces to the square root of the product of the operators if the operators commute. Finally, by using the geometric mean, an operator version of the Gaussian mean is presented.
RESUMO
A new Hermitian semidefinite matrix operation is studied. This operation-called parallel subtraction-is developed from the theory of parallel addition. Since the theory of parallel addition is motivated by the analysis of interconnected electrical networks, parallel subraction may be interpreted in terms of the synthesis of electrical networks. The idea of subtraction is also extended to hybrid addition.