*Abstract:* |
Most algebraists believe they know Linear Algebra. The purpose of this talk is to indicate that this
is not necessarily true. We show a substantial amount of "new" Linear Algebra and
its connection to Algebraic Geometry, in particular to the theory of zero-dimensional subschemes
of affine spaces, and to Computer Algebra, in particular to the task of solving zero-dimensional
polynomial systems. Here are some questions which we will answer in this talk: What are the
big kernel and the small image of an endomorphism? What are its eigenspaces and generalized
eigenspaces if it has no eigenvalues? What is the kernel of an ideal? What is a commendable
endomorphism? And what is a commendable family of endomorphisms? How is this connected to
curvilinear and Gorenstein schemes? And how can you use this to solve polynomial systems? |