The most efficient way to calculate multiplication and summation of two large matrices

Support I have two matrices and , I would like to calculate following:

where matrix , and represent each columne of two matrices

I was wondering, what is the most efficient way to calculate matrix C? Many thanks!

Answer 1

[Bruno Luong]

It is just a scaling of matrix multiplication, if you haven't recorgnize it

A=rand(300,1000);
B=rand(300,1000);

tic
C1=(A*B')/size(A,2);
toc

Elapsed time is 0.003844 seconds.

% or
tic
C2 = sum(pagemtimes(reshape(A,size(A,1),1,[]),reshape(B,1,size(B,1),[])),3)/size(A,2);
toc

Elapsed time is 0.186097 seconds.

% or
tic
C3 = sum(reshape(A,size(A,1),1,[]).*reshape(B,1,size(B,1),[]),3)/size(A,2);
toc

Elapsed time is 0.192863 seconds.

norm(C1-C2,'fro')

ans = 6.1978e-14

norm(C1-C3,'fro')

ans = 6.1978e-14

[Mingyang Sun]

I am so sorry for my stupid question................ yes, C = A*B.'