# Column multiplication of two 2D matrices.

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Nikan Fakhari on 13 Jan 2021
Edited: Bruno Luong on 14 Jan 2021
Hi there,
I have two quite large matrices with the following sizes:
A = rand(94037,2240) B=rand(2240,2240)
I would like to mutiply each column of A by the transpose of each column of B (bascially two vector multiplication). Therefore each mutiplcation gives me a 2D matrix wih size (94037,2240) and I would like to store the result of each multiplication in a 3d MATRIX.
The thing is I can do this with for-loop as show below but its very slow and in the middle of operation matlab exist, because its quite heavy.
S = zeros(94037,2240,2240);
for i=1:1:2240
S(:,:,i) =A(:,i)*(B(:,i))';
end
Is there anyway I can do this without using for loop to speed up the process ?
Thanks for the help.
Best,
Nikan
##### 2 CommentsShowHide 1 older comment
Nikan Fakhari on 13 Jan 2021
I am planning to take sum along the third dimension

Matt J on 13 Jan 2021
Edited: Matt J on 13 Jan 2021
I am planning to take sum along the third dimension
That would simply give you A*B.'

Matt J on 13 Jan 2021
Edited: Matt J on 14 Jan 2021
I doubt you will be able to do the computation with the matrix sizes you've indicated. The result will consume 3.5 TB of RAM in double floating point. However, if you can scale down the matrix sizes, then a loop-free solution is as follows,
[ma,na]=size(A);
[mb,nb]=size(B);
S=reshape(A,ma,1,na).*reshape(B,1,mb,nb);
##### 2 CommentsShowHide 1 older comment
Matt J on 14 Jan 2021
Right!