# How to vectorize the multiplication of arrays with DIM=5?

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AP on 29 May 2014
Edited: AP on 29 May 2014
I have a three dimensional domain in MATLAB. For each point in the domain I have defined three arrays of size (NX,NY,NZ) at each point of the domain:
A1; % size(A1) = [NX NY NZ]
A2; % size(A2) = [NX NY NZ]
A3; % size(A3) = [NX NY NZ]
For each element, I am trying to construct an array which holds the value of A1, A2, and A3. Would the following be a good candidate for having a 1×3 vector at each point?
B = [A1(:) A2(:) A3(:)];
B = reshape(B, [size(A1) 1 3]);
If the 1×3 array is named C, I am trying to find C'*C at each point.
C = [A1(i,j,k) A2(i,j,k) A3(i,j,k)]; % size(C) = [1 3]
D = C'*C; % size(D) = [3 3]
My ultimate goal is to find the array D with size 3×3 for all the points in the domain in a vectorize fashion? Could someone help me?

Matt J on 29 May 2014
Are you sure you don't mean the inner product
C(i,j,k) = [A1(i,j,k) A2(i,j,k) A3(i,j,k)]*[A1(i,j,k) A2(i,j,k) A3(i,j,k)]'
The expression you have is a non-scalar, outer product and cannot be assigned to a scalar location C(i,j,k).
AP on 29 May 2014
Sorry for the confusion. I am not looking for inner product. I have updated my question and explained it in a better way.