Consider the 4 x 4 covariance correlation matrix of example

Question

Consider the (4 X 4) covariance (correlation) matrix of Example 3.2. Verify the results of Theorem 3.8. Also verify that latent vectors of P are orthogonal unit vectors.

Example

The starting point for a PCA of an infinite population is a dispersion matrix of the variates, usually Σ or P. Consider four random variables X₁, X₂, X₃, and X₄ with covariance matrix

THEOREM

Let Σ be a ( p x p) covariance matrix with latent roots Λ and latent vectors Π. Then Σ^-1 possesses latent roots Λ^-1and latent vectors Π.