This problem comes from Bayesian statistics, where N is number of observations and F is number of factors. All of the Sigma (Σ) are variance-covariance matrices. The Greek characters after each Σ are meant to be subscripts.
I am having trouble proving that two multivariate formulas are equivalent. I implemented them in MATLAB and numerically they appear to be equivalent.
I would appreciate any help on this.
Prove A = B
A = (Σπ^-1 + Σy^-1)^-1 * (Σπ^-1*π + Σy^-1*y)
y = π+ X*β
Σπ =τ*Σ
Σy = X' * Σβ * X + ΣεB =...