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

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Tommaso Delicato
Tommaso Delicato 2021-2-1
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

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