MATLAB: Row by column multiplication

vectorization

Consider two matrices A and B defined by
A=rand(10,3);
B=rand(3,10);
I'm interested in multiplying the vectors defined the first, second, and third rows in B by the vectors defined the first, second, and third columns in A, respectively. My intent is to generate ten, 3X3 matrices defined by
Matrix1= B(:,1)*A(1,:)  
Matrix2= B(:,2)*A(2,:)
...
Matrix10= B(:,10)*A(10,:)
My initial thought was something like
B(:,1:10)*A(1:10,:)
but this approach populates the matrices B and A prior to multiplication, yielding a single 3X3 matrix. How to I change the "order-of-operations" if you will—call each vector on a term-by-term basis, multiplying in between each call to generate the desired matrix? Of course, I really want to avoid having to use for loops.

Best Answer

Here's a completely vectorized method, which requires James Tursa's MTIMESX function, available at the link below
A=reshape(A',1,3,10);
B=reshape(B,3,1,10);
C=mtimesx(B,A)
http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support
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