# Monthly Archives: February 2020

## Derivation: Wilk’s $\Lambda$ as $\prod \frac{1}{1+\lambda_i}$.

Show that Wilk’s $\Lambda$ can be represented as $\Lambda = \frac{|E|}{|E+H|} = \prod_{1=1}^s\frac{1}{1+\lambda_i}$, where $\lambda_i$ is the eigenvalues of $E^{-1}H$. Proof: $\frac{|E|}{|E+H|} = \frac{|E|/|E|}{|E+H|/|E|} = \frac{1}{|E^{-1}E+E^{-1}H|} = \frac{1}{|I+E^{-1}H|}$ Now suppose $\mu$ as an eigenvalue of $|I+E^{-1}H|$,… Read more »