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So what would be the $U$ matrix in FactoMineR representing differently from that of the svd? How to make them match up using R? … Apart from the signs, it seems that the $V$ matrix is the same for the two function outpus, but what makes the $U$ different then between them? …

The difference between FactoMineR:::PCA() and base::svd() is the scaling and negative signs for some columns in the dataset. The below code is a proof of the above: # PCA using FactoMineR::PCA() libra …

identity matrix for Sigma prcomp.pca$rotation %*% t(prcomp.pca$rotation) # identity matrix for V # now compute the U matrix from prcomp() output per the equation above for U prcomp.pca$u <- S %*% (solve … So the computed $U$ matrix eventually didn't match the $U$ matrix of the svd() function, what am I missing here to obtain the $U$ matrix from the output of prcomp()? …

code of prcomp() this can be achieved by the following: sigma <- prcomp.pca$sdev * sqrt(max(1, nrow(S) - 1)) round(sigma, 2) == round(svd.pca$d, 2) # TRUE diag(sigma) %*% solve(diag(sigma)) # identity matrix … of Sigma prcomp.pca$rotation %*% t(prcomp.pca$rotation) # identity matrix of V prcomp.pca$u <- S %*% prcomp.pca$rotation %*% solve(diag(sigma)) round(svd.pca$u, 3) == round(prcomp.pca$u, 3) # TRUE …