How to do row vector matrix multiplication using dot products
Let’s explore the definition of row-vector-matrix multiplication via dot products:
00:00 -Introduction
00:25 -Let A be a real-valued matrix with m rows and n columns
00:35 -Let x be a column vector with m rows and 1 column
00:47 -The output of the row-vector-matrix product via dot products
01:22 -The kth entry is the dot product of x with the kth column of A
02:03 -Analyze the dimensions : the inner dimensions must agree
03:04 -For row-vector-matrix multiplication, partition matrix into columns
04:04 -Calculate the first entry of the output vector
05:11 -To grow your brain, engage in repeated deliberate practice
05:22 -Calculate the second entry of the output vector
07:05 -Let’s find a pattern
07:46 -Calculate the last entry of the output vector
08:05 -Great math habit: do some base cases then make a guess and verify
08:21 -Put it all together
09:04 -Transition to scalarized to vectorized information
10:07 -Factor out individual entries in linear combination approach
10:31 -Same as row-vector-matrix multiplication via linear combinations
11:18 -Anatomy of the row-vector-matrix multiplication via dot products
11:41 -Slice output vector b into individual scalars
11:48 -Partition the modeling matrix into individual columns
12:20 -Challenge: how do matrix partitions show up in matrix-vector multiplication
13:22 -Conclusion