New article series at catonmat: Detailed Summary of MIT's Linear Algebra

MIT's does happen to be available on the internet...

I've watched some of the lectures, and Strang's teaching skills are outstanding.

I don't know why I care. MIT just sounds impressive.

I wouldn't say that research skills are not important. For example, the algorithms course at MIT included a very modern topic on "cache oblivious algorithms", which was developed there just a few years ago by the same professor who taught the course. It would take some years for the other better educators to learn how to teach it.

Same with linear algebra, here in Latvia we had a great professor who taught it, but he never mentioned even jpeg compression or any other modern stuff that Gilbert Strang does. We got taught the regular stuff that has been around in linear algebra for 100 years.

The article seems to answer the question:

I had already had two terms of linear algebra when I studied physics back in 2004. But it was not enough for a curious mind like mine. I wanted to see how it was taught at the world’s best university.

...and...

The course is taught by no other than Gilbert Strang. He’s the world’s leading expert in linear algebra and its applications and has helped the development of Matlab mathematics software.

Based on my observations, experience, and intuition, I've found that a fundamental clarity of mind is extremely useful in trying to do good research and is the basic skill you need to be a good teacher. It follows that, statistically, most top researchers have at least the ability to be good teachers, if not the desire.

Now, being a top researcher takes more than just clarity of mind, so many people with enormous teaching abilities don't have the skill set to be an MIT professor, but I do think that MIT indirectly selects for good teaching.