matrix multiplication for "3-D" matrices

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i have 8 vectors a11, a12, a21, a22 and b11, b12, b21, b22 let's say of length 1x100. i want to do a*b matrix multiplication for the 2x2 matrices [a11 a12; a21 a22] and [b11 b12; b21 b22] and along the dimension of length 100. how to code this without using do loops?

Accepted Answer

Matt J
Matt J on 6 Sep 2019
result(1,1,:)=a11.*b11 + a12.*b21;
result(1,2,:)=a11.*b12 + a12.*b22;
result(2,1,:)=a21.*b11 + a22.*b21;
result(2,2,:)=a21.*b12 + a22.*b22;
Matt J
Matt J on 6 Sep 2019
You're welcome, but please Accept-click the answer if you are satisfied with it.

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More Answers (2)

Fabio Freschi
Fabio Freschi on 6 Sep 2019
Let's start saying that the data structure you are using is not the best one. See
If you really want to keep that structure, maybe the simplest answer is to make the manual multiplication
C = A*B <- matrix form
c11 = a11*b11+a12*b21 <- element form
since you have array, use .* operator
c11 = a11.*b11+a12.*b21
Note that this works only for 2x2 matrices.
For a more general approach, see
MURTY KOMPELLA on 6 Sep 2019
Hello Fabio, now (using arrayfun) you are going above my comfort level lol! This is very interesting, let me look into it, Thanks!

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Catalytic on 6 Sep 2019
If you have the parallel computing toolbox, you can do this on the GPU with
but this may only provide gains if the pages A(:,:,i) and B(:,:,i) are large matrices.
  1 Comment
MURTY KOMPELLA on 6 Sep 2019
Hello Sir, thanks for your answer. I do not have this toolbox.

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