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Lec 24 MIT 7.012 Introduction to Biology, Fall 2004

It comes acquainted with different antigens. And recall that what we were talking about was the following, that there were several kinds of phagocytic cells. Phagocytic cells are cells that chew up other things, both macrophages and even more frequently, dendritic cells, many of which hang around lymph nodes by the way. They process antigens into oligopeptides. The oligopeptides get presented on the surface of these cells. Let's say, here's a macrophage, in the form of through the class 2 MHC molecules which are displayed on the surfaces of the cells. And, here's a typical oligopeptide that has been chewed up from one of the antigens that was previously internalized, eaten up by the macrophage, a dendritic cell, and then presented on the surface. Recall, then, we have an itinerant macrophage or dendritic cell. Could we turn up the sound just a little, just a notch? Thank you. And this dendritic cell or macrophage...

Eigenfunctions of a Hermitian operator

PROFESSOR: So here comes the point that this quite fabulous about Hermitian operators. Here is the thing that it really should impress you. It's the fact that any, all Hermitian operators have as many eigenfunctions and eigenvalues as you can possibly need, whatever that means. But they're rich. It's a lot of those states. What it really means is that the set of eigenfunctions for any Hermitian operator-- whatever Hermitian operator, it's not just for some especially nice ones-- for all of them you get eigenfunctions. And these eigenfunctions, because it has vectors, they are enough to span the space of states. That is any state can be written as a superposition of those eigenvectors. There's enough. If you're thinking finite dimensional vector spaces, if you're looking at the Hermitian matrix, the eigenvectors will provide you a basis for the vector space. You can understand anything in terms of eigenvectors. It is such an important theorem. I...