extract the j-th component of the vector resulting from the matrix product.

I cannot code the fact that I have to extract the j-th component from the vector that results from a matrix product in a constrained minimization problem.

Minimize ∑(RC(Fj)/σP−1/M)^2 for j=1:M

sub ∑x=1

where RC(Fj) = (A⊤x)j⋅ (A+Σx/√x⊤Σx)j

where

• A is a loadings matrix
• A+ is Moore-Penrose inverse of A
• Σ is a covariance matrix
• x is a weights vector

I should therefore extract the j-th component of the following matrix products

(A⊤x)j

(A+Σx/√x⊤Σx)j