Re:Matrix Multiplication
by JabavuAdams on Friday November 25, 2016 @05:27PM
(#13040308)
Neat visualization. I feel it's important and eye-opening to note that there's not just one way to multiply matrices, there're five (according to Strang):
5 ways to multiply A B = C
1) Each element of C is a dot-product of corresponding rows of A with columns of B
2) Each column of C is a combination of the columns A. Each column of B has the coefficients.
3) Each row of C is a combination of the rows of B. Each row of A has the coefficients.
4) Accumulate outer-product. Accumulate sums of of outer-products of each col of A with each row of B.
5) Block multiplication
They all produce the same answer, but different ones provide different insight for particular situations.
5 ways to multiply A B = C
1) Each element of C is a dot-product of corresponding rows of A with columns of B
2) Each column of C is a combination of the columns A. Each column of B has the coefficients.
3) Each row of C is a combination of the rows of B. Each row of A has the coefficients.
4) Accumulate outer-product. Accumulate sums of of outer-products of each col of A with each row of B.
5) Block multiplication
They all produce the same answer, but different ones provide different insight for particular situations.
See Video Lecture #3 of Strang's Linear Algebra course for more info: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...