What is the relationship between matrix-vector multiplication and matrix partitions?
We investigate the relationship between matrix-vector multiplication and matrix partitions.
00:00 -Introduction
00:11 -Matrix-vector multiplication is two different operations
00:18 -Matrix-column-vector multiplication
00:40 -Row-vector-matrix multiplication
01:00 -For each operation, we have two different approaches
01:04 -Vectorized version of matrix-column-vector multiplication
01:22 -Scalarized version of matrix-column-vector multiplication
01:37 -Hint for our desired relationship
01:52 -Vectorized version of row-vector-matrix multiplication
02:13 -Scalarized version of row-vector-matrix multiplication
02:30 -Difference between linear combination and dot product definitions
02:44 -The anatomy of matrix-vector multiplication
03:14 -Questions to identify patterns in partitions and operation structure
03:25 -Question 1: Is the modeling matrix the left factor or the right factor?
03:32 -Question 2: Do we want to vectorize or scalarize the output?
03:52 -Table of four different options of answers for these questions
04:21 -Option 1: Modeling matrix on left and data is vectorized
05:14 -Option 2: Modeling matrix on left and data is scalarized
06:05 -Option 3: Modeling matrix on right and data is vectorized
06:58 -Option 4: Modeling matrix on right and data is scalarized
07:40 -Relationship between partitions and matrix-vector multiplication
08:38 -Challenge: How are matrix partitions related to computer science?
09:19 -Conclusion