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Invariants of 2 x 2-MatricesLarry Smith, Gottingen and Yale UniversityMonday, April 24 at 4:45-5:45PMHylan 1101 Let T: C2 to C2 be a linear transformation of the 2-dimensional complex vector space V = C2 into itself. If we choose a basis for V, say the standard basis, or some other basis, any basis will do, then we can represent T by a 2 x 2 matrix
with entries which are complex numbers. Changing the basis changes the matrix. What functions of the four matrix entries remain invariant under change of basis? It is easy enough to think of a couple that do: for example the trace
and the determinant
to name just a few. If by function we understand polynomial, then in fact in some sense (to be made precise in the talk) these are in fact all such functions. But what happens if we change the ground field from the complex numbers C to a finite field? The situation here is full of suprises and I will try to explain how this works out.
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