Let C1,…,Ce be noncentral conjugacy classes of the algebraic group G=SLn(k) defined over a sufficiently large field k, and let Ω:=C1×…×Ce. This paper determines necessary sufficient conditions for existence tuple (x1,…,xe)∈Ω such that 〈x1,…,xe〉 is Zariski dense in G. As consequence, new result concerning generic stabilizers linear representations groups proved, existing results on random (r,s)-...

Linear sjstem realization problems require the construction of a linear system realiization, or a quadruple of real matrices F,G, H, J, of a given real rational W ( s ) , so ithat W(s) = J + H'(sI F)-'G. When W(s) has certain properties, corresponding ;to symmetry, passivity, or losslwness, it is possible to select a realization that closely (but not necessarily exactly) reflects thesepropertie...