PCA / FA Example 7: Bartholomew et al. Calculations

The familiar part

This is the second post about Example 7. We confirm their analysis, but we work with the computed correlation matrix rather than their published rounded-off correlation matrix.

I am pretty well standardizing my notation. V is an orthogonal eigenvector matrix from an eigendecomposition; \lambda is the associated eigenvalues, possibly as a list, possibly as a square diagonal matrix. \Lambda is the square roots of \lambda\ , possibly as a list, possibly as a square matrix, and possibly as a matrix with rows of zeroes appended to make it the same shape as w (below).

Ah, X is a data matrix with observations in rows. Its transpose is Z = X^T\ .

The (full) singular value decomposition (SVD) is the product u\ w\ v^T\ , with u and v orthogonal, w is generally rectangular, as it must be the same shape as X.
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