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)-...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

We present a new algorithm to decide whether two rational parametric curves are related by a projective transformation and detect all such projective equivalences. Given two rational curves, we derive a system of polynomial equations whose solutions define linear rational transformations of the parameter domain, such that each transformation corresponds to a projective equivalence between the t...