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class -- In the last we lecture traditionally we bring in a guest lecturer to tell us of their perspective on complex systems and it is with great pleasure to welcome Hal Albelson. A professor here at MIT for many years, some of you might have already taken classes from him. And what he is going to talk about is a topic we've touched upon, but not in particular detail, in the first two lectures. In particular the interaction of technology and complex systems with law and social issues. Hal: Ok, thanks. Okay hi. Hari asked me to talk about complex systems, which is kind of what you've been studying all semester. Today I want to give you of a hint of another kind of complexity. You have been doing the technical infrastructure for essentially what has become the information age. But the information age... You gotta turn off the mic. But the information age has just changed the world immensely over the last 20 years and has run smack into another kind of complexity. A...

-- one and -- the lecture on symmetric matrixes. So that's the most important class of matrixes, symmetric matrixes. A equals A transpose. So the first points, the main points of the lecture I'll tell you right away. What's special about the eigenvalues? What's special about the eigenvectors? This is -- the way we now look at a matrix. We want to know about its eigenvalues and eigenvectors and if we have a special type of matrix, that should tell us something about eigenvalues and eigenvectors. Like Markov matrixes, they have an eigenvalue equal one. Now symmetric matrixes, can I just tell you right off what the main facts -- the two main facts are? The eigenvalues of a symmetric matrix, real -- this is a real symmetric matrix, we -- talking mostly about real matrixes. The eigenvalues are also real. So our examples of rotation matrixes, where -- where we got E- eigenvalues that were complex, that won't happen now. For symmetric matrixes, the eigenvalue...

-- valuable experience. OK, today we're going to start talking about a particular class of algorithms called greedy algorithms. But we're going to do it in the context of graphs. So, I want to review a little bit about graphs, which mostly you can find in the textbook in appendix B. And so, if you haven't reviewed in appendix B recently, please sit down and review appendix B. It will pay off especially during our take-home quiz. So, just reminder, a digraph, what's a digraph? What's that short for? Directed graph, OK? Directed graph, G equals (V,E), OK, has a set, V, of vertices. And, I always get people telling me that I have one vertice. The singular is not vertice; it is vertex, OK? The plural is vertices. The singular is vertex. It's one of those weird English words. It's probably originally like French or something, right? I don't know. OK, anyway, and we have a set, E, which is a subset of V cross V of edges. So that's a digraph. ...