# Vectorization of matrices multiplication

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Eugenio Grabovic on 21 Jan 2019
Commented: Eugenio Grabovic on 21 Jan 2019
Hi,
i have some trouble finding out how to vectorize the following loop:
for k = 1:PointsLength
h(k,1) = transpose(PointsA(:,k) - PointsB(:,k))*normals(:,k);
end
The first thing that comes into my mind is doing this:
all the matrices have 3 x n dimensions and i want h to be 1 x n vector
k = 1:PointsLength
h(:) = transpose(PointsA(:,k) - PointsB(:,k))*normals(:,k);
but its obviously it's not the same thing since im trying to achieve row column multiplication only in pairs ( just k_th row times k_th column, without k_th row times other columns), and thus gives error cause he expects h to be n x n.
Any ideas? Thank you in advance.

madhan ravi on 21 Jan 2019
Probably you want to use .* (element-wise multiplication) ?
Eugenio Grabovic on 21 Jan 2019
k = 1:PointsLength
h(:) = transpose(PointsA(:,k) - PointsB(:,k)).*normals(:,k);
gives error cause he wants matrices to have the same dimensions (no transpose),
but by doing that i would only achieve (i_th,j_th) element multiplication only, with a 3 x n h matrix as a result (not what i was looking for).

Jan on 21 Jan 2019
Edited: Jan on 21 Jan 2019
h = dot(PointsA - PointsB, normals).'
or
h = sum((PointsA - PointsB) .* normals, 1).'

#### 1 Comment

Eugenio Grabovic on 21 Jan 2019
Oh wow, i feel so stupid... thank you very much !