PCA / FA Example 9: scores & loadings

I want to look at reconstituting the data. Equivalently, I want to look at setting successive singular values to zero.

This example was actually built on the previous one. Before I set the row sums to 1, I had started with

t1 = \left(\begin{array}{lll} 1 & 1 & -3 \\ -1 & 2 & -2 \\ 1 & 3 & -1 \\ -1 & 4 & 1 \\ 1 & 5 & 4\end{array}\right)

I’m going to continue with Harmon’s & Bartholomew’s model: Z = A F, Z = X^T, X is standardized, A is an eigenvector matrix weighted by the square roots of the eigenvalues of the correlation matrix of X.

I want data with one eigenvalue so large that we could sensibly retain only that one. Let me show you how I got that.
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