Lecture 42. Invariant Subspaces скачать в хорошем качестве

Lecture 42. Invariant Subspaces

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.