H-alpha decomposition

H-\(\alpha\) decomposition is based on the eigenvalue/eigenvector decomposition of the T3 matrix.

The eigenvalues from the H-\(\alpha\) decomposition are used to calculate entropy. Entropy function
$$H=\sum^3_{i=1}p_ilog_3p_i$$
Where \(0\leq H\leq 1\) and
$$p_i=\frac{\lambda_i}{\sum^3_{q=1}\lambda_q}$$
The eigenvectors contain the parameter \(\alpha\) which represents the dominant scattering mechanism.
$$\alpha=\sum^3_{i=1}p_i\alpha_i$$
Where \(0\leq\alpha\leq\frac{\pi}{2}\)