How to do matrix matrix multiplication using dot products?
We develop our third of four different techniques to calculate a matrix-matrix multiplication (MMM). In this case, we calculate the individual entries of the product of two matrices using dot products.
00:00 -Introduction
00:21 -Definition of matrix-matrix multiplication via dot products
02:12 -When reading formal math, deep read with paper and pencil
02:52 -The anatomy of a matrix-matrix multiplication via dot products
03:06 -The dot product version of MMM is great to find individual entries
03:37 -MMM via dot products cut left matrix in rows right matrix in columns
04:02 -Analysis: row partition left matrix and column partition right matrix
05:27 -Apply definition 5.3 to calculate entry (1,1) of a general MMM
08:29 -Apply definition 5.3 to calculate entry (2,1) of a general MMM
08:43 -Push pause and try to finish this for yourself
11:12 -Pause the video and guess the general pattern for entry (i, k)
11:41 -Apply definition 5.3 to calculate entry (1,2) of a general MMM
13:50 -To learn math deep, develop multiple representations
14:25 -Guess pattern for entry (i, k) and discover definition 5.3 for ourselves
17:24 -Use MMM via dot products to find individual entries of output
18:02 -Challenge 1: Make a “cheat sheet” for our three versions of MMM
18:59 -For my students: NO timed exams use any resource you want to learn
15:04 -Conclusion