Invariant Subspaces of Linear Operators and the Eigenvalue Problem

We discuss the idea of an invariant subspace of a linear operator. These are subspaces that the operator maps back into itself. It is always the case that the kernel and image of the operator are subspaces, but we are interested in the question of the one dimensional invariant subspaces. These are the subspace which lead us to the eigenvalue problem. #mikethemathematician, #mikedabkowski, #profdabkowski