Right, left characteristic sequences and column, row minimal indices of a singular pencil
N. Karcanias, G. Kalogeropoulos · International Journal of Control · 1988
For a general singular pencil sF — G∊ℝ m×n [s] the right, left characteristic sequences r(F, G), l(F, G) are defined and they are shown to be of the piecewise arithmetic progression type. The sets of column, row minimal indices ℐc(F, G), ℐr(F, G) are defined by a singular points analysis of r(F, G), ℐl(F, G) respectively. Thus, ℐc(F, G), ℐr(F, G) emerge as numerical invariants of the ordered pair (F, G) and they may be computed by rank tests on Toeplitz matrices defined on (F, G).