I'm currently studying matrix operations, and one of the techniques for multiplication is matrix partitioning. While I understand the concept of partioning the matrix into row or column vectors, I don't understand this other technique of partitioning a matrix into sub-matrices of different sizes. Can someone help me explain the logic behind this and how it's used?
#Help with Linear Algebra
radiant herald
quasi pierBOT
I'm currently studying matrix operations, and one of the techniques for multipli...
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radiant herald
crimson sail
The (i,j)-th entry of the resultant matrix of multiplying two compatible matrices together is the dot product of the i-th row of the first matrix and the j-th column of the second matrix
which is essentially summing products of pairs of scalars
Partitioning either multiplicand/multiplier into submatrices merely groups up the scalars into different sets. Addition between scalars is associative.
radiant herald
I see, but how does partitioning help in multiplication?
Let's say I have this matrix:
1 2 3 4
5 6 7 8
9 0 1 2
and I wanna multiply it to
1
2
3
4
How does the first partitioning technique apply in this case?
grim nacelleBOT
@radiant herald