Okay.
This is lecture five in linear algebra.
And, it will complete this chapter of the book.
So the last section of this chapter is two point seven that talks about permutations, which finished the previous lecture, and transposes, which also came in the previous lecture.
There's a little more to do with those guys, permutations and transposes.
But then the heart of the lecture will be the beginning of what you could say is the beginning of linear algebra, the beginning of real linear algebra which is seeing a bigger picture with vector spaces -- not just vectors, but spaces of vectors and sub-spaces of those spaces.
So we're a little ahead of the syllabus, which is good, because we're coming to the place where, there's a lot to do.
Okay.
So, to begin with permutations.
Can I just -- so these permutations, those are matrices P and they execute row exchanges.
