# Matrix Multiplication & Splitting

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Rahul Marwaha on 19 Feb 2021
Answered: James Tursa on 19 Feb 2021
Hi I'm trying to extract given values from a large matrix and mulitply it by other known matrices e.g.
A = [1 2 3: 4 5 6: 7 8 9] % 3x3 Matrix which is always the same
B = [1 2 3] % 3x1 Matrix which also stays the same
C = % A matrix of 3x12 or 3x15 etc, e.g. The matrix could be split into indiviudal 3x3 matrices
As shown above I compute the matrix C which is formed from varying numbers of 3x3 matrices. I'm then attempting to call each 3x3 from the matrix and multiply it by the A and B e.g.
D1 = A * B * C(:,1:3)
D2 = A * B * C(:,4:6)
D3 = A * B * C(:,7:9) % etc until I have done it for all the sub 3x3 matrices
As shown the large matrix C is split into equal 3x3 matrices and then is multiplied by A and B. I was wondering how this could be done for C being any 3 by matrix e.g. 3x12 or 3x36 i.e. it can be evenly split into individual 3x3 matrices.
Any help is greatly appreciated, thanks!
Steven Lord on 19 Feb 2021
If you adopt the approach suggested by the other posters and turn your C matrix into a 3-dimensional array D, in release R2020b and later you could use the pagemtimes function to compute the product of your A matrix with each page of D.

Ive J on 19 Feb 2021
Edited: Ive J on 19 Feb 2021
Given your input criteria, you can simply reshape C:
sz = size(C, 2);
C = reshape(C, 3, 3, sz/3);
D = arrayfun(@(i)A*B*C(:,:,i), 1:sz/3, 'UniformOutput', false);
Rahul Marwaha on 19 Feb 2021
Thank you so much, I apologise it should have been as you've shown I totally forgot the order of multiplicaiton that would render the calculation impossible.

James Tursa on 19 Feb 2021
Based on your latest posts, it sounds like you really want A*C(3x3 slice)*B. So again it would be nice to do all the multiplies in one fell swoop and then pick off your desired results. E.g.,
D = B.' * reshape(permute(reshape(A*C,3,3,[]),[2 1 3]),3,[]);
D = reshape(D,3,[]);
and the results are in D(:,1), D(:,2), etc.
Or just use the following as Steven Lord suggests:
D = pagemtimes(reshape(A*C,3,3,[]),B);

James Tursa on 19 Feb 2021
Edited: James Tursa on 19 Feb 2021
Your dimensions don't work. A*B is going to be 3x1. You can't multiply this by a 3xN matrix.
That being said, suppose you did have dimensions that did work for A*B. Then you don't need to split anything up for the multiply. You can just do A*B*C directly and then pick off the columns of the result that you want. E.g., suppose we have the simpler problem below
A is 3x3
C is 3x12
and we want A multiplied by individual 3x3 parts of C. Then instead of doing these individual matrix multipies
D1 = A*C(:,1:3)
D2 = A*C(:,4:6)
D3 = A*C(:,7:9)
D4 = A*C(:,10:12)
You can just do this all in one fell swoop
D = A*C
and then reshape it for convenience
D = reshape(D,3,3,[])
Then you can pick off D(:,;1), D(:,:,2), etc. for your results.
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James Tursa on 19 Feb 2021
If B is really 1x3 and the order is supposed to be B*A*C(:,slice), then it is just
D = B*A*C;
Then you can reshape
D = reshape(D,1,3,[]);
and you can pick off D(:,:,1), D(:,:,2), etc. for the results.