Lecture 12: Introduction to Matrix Multiplication (Nicholson Section 2.3)
Sub Project: Linear Algebra Lecture Videos
Alternate Video Access via MyMedia | Video Duration: 13:46
Description: Started with a review of an earlier example that motivated matrix-vector multiplication.
3:50 -- Introduced matrix multiplication. Just because AB is defined, doesn’t mean that BA is defined.
4:50 --- And even if they’re both defined, it doesn’t mean that AB=BA. AB and BA might not even be the same size.
9:15 --- In general, matrix multiplication doesn’t commute --- the order matters! Even if AB and BA are the same size.
11:00 --- Did an example showing what happens when you multiply a matrix by a diagonal matrix. This is an important example to remember.
12:10 --- For real numbers you know that ab = ac implies b=c only if a is nonzero. Similarly, if AB=AC this doesn’t always imply that B=C. But it's even trickier --- it's not just a matter of having to worry about the possibility that A might be an all-zero matrix. Gave an example of a nonzero matrix A such that AB=AC but B doesn’t equal C.
