Seminar by Professor Michael Karow

Venue: MZ 195, Committee Room, Department of Mathematics
Time: 4pm
Date: 26.03.2019 (Tuesday)

Speaker: Professor Michael Karow
(Department of Mathematics, TU Berlin, Germany)

Title: Projection Lemma and the Cyclic Decomposition Theorem
One of the fundamental results of Linear Algebra is the Cyclic Decomposition Theorem. Let $A:X o X$ be a linear operator on a finite dimensional vector space $X$ over a field $F$. The theorem states that $X$ is a direct sum of $A$ invariant subspaces which are generated by a single vector. The special case that $F$ is the field of complex numbers yields the Jordan Canonical Form. We present a short proof of the Cyclic Decomposition Theorem using a result on projections.