Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also an...

Participation factors are nondimensional scalars that measure the interaction between the modes and the state variables of a linear system. Since their introduction by Verghese, Pérez-Arriaga and Schweppe, participation factors have been used for analysis, order reduction and controller design in a variety of fields. In this paper, participation factors are revisited, resulting in new definitio...