Covariance matrix with latent roots ? and latent vectors

Reference no: EM131059916

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.

Reference no: EM131059916

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