Example 1 of matrix matrix multiplication via linear combinations of rows
We do our first example of left matrix-matrix multiplication (MMM) to scale each row of a matrix with a unique scalar value.
00:00 -Introduction
00:22 -Problem statement: scale each row by a specific value
00:40 -To do work on the row, multiply modeling matrix on the left
01:24 -Use a transposition matrix to swap columns
01:44 -Scale the rows of a modeling matrix by left MMM by a diagonal matrix
02:21 -Calculate row 1: left MMM via linear combinations of row vectors
02:33 -Pause video: recall def of left MMM via linear combo of row vectors
02:42 -Let’s do this together: calculating row 1
02:57 -Test yourself on definition of row-vector matrix multiplication
03:52 -Calculate row 2: left MMM via linear combinations of row vectors
05:27 -Calculate row 3: left MMM via linear combinations of row vectors
07:22 -Calculate row 4: left MMM via linear combinations of row vectors
08:06 -Combine all results together to form product
09:16 -Intuition: to do
09:48 -Challenge 1: Show diagonal matrix is product of four dilation matrices
10:26 -Challenge 2: Show dilation matrices are commutative under MMM
10:42 -Challenge 3: Is matrix-matrix multiplication commutative?
11:27 -Conclusion