To begin our study, we will look at subspaces \(U\) of \(V\) that have special properties under an operator \(T\) in \(\mathcal{L}(V,V)\). That is, \(U\) is invariant under \(T\) if the image of every...To begin our study, we will look at subspaces \(U\) of \(V\) that have special properties under an operator \(T\) in \(\mathcal{L}(V,V)\). That is, \(U\) is invariant under \(T\) if the image of every vector in \(U\) under \(T\) remains within \(U\). An important special case of Definition 7.1.1 involves one-dimensional invariant subspaces under an operator \(T\) in \(\mathcal{L}(V,V)\).
