0:00 What is an invariant subspace for a linear operator?
1:52 Examples of invariant subspaces
7:06 Invariant subspaces correspond to a block of zeros in a matrix
11:58 For a pair of commuting operators T, S, the kernel of S is invariant under T
16:48 A pair of commuting operators on a complex vector space have a common eigenvector
21:45 Structure of invariant subspaces for a diagonalizable operator
31:05 Simultaneous diagonalization of commuting operators
In this lecture, we introduce the notion of an invariant subspace for a linear operator and classify invariant subspaces of diagonalizable operators.
This is a lecture in a "Linear Algebra" course for students specializing in mathematics.
