Replacing a for loop with matrix multiplication

In the problem I have here, x is a 2x300 matrix and SIG is a 2x2 matrix.

What I'm looking for is a 1x300 vector, where the ith entry corresponds to x(:,i)'*inv(SIG)*x(:,i). I've written this out in a for loop below:

ans = zeros(1,size(x,2));
for i = 1:size(x,2)
    ans(i) = x(:,i)'*inv(SIG)*x(:,i);
end

but I think there must be a way to make this more efficient with some sort of matrix multiplication--I just can't figure it out.

Any help appreciated!

[Stephen23]

Note that using inv is less efficient than using mldivide:

https://www.mathworks.com/help/matlab/ref/inv.html#bu8tv8c-6

Answer 1

[James Tursa]

result = sum(x.*(inv(SIG)*x));

or

result = sum(x.*(SIG\x));

[Bruno Luong]

In case complex data

result = sum(conj(x).*(SIG\x));

Answer 2

[J Chen]

Try x'*inv(SIG)*x. Matlab can directly handle vectors and matrices.