General matrix-normal α-divergence formula

Derive the explicit α-divergence formula for matrix-normal distributions when both covariance factors and the mean vary, and extend the associated α-connection analysis to the full matrix-normal family.

Background

For matrix-normal distributions with fixed covariance factors, the paper proves that the α-divergence is independent of α and has a simple quadratic form in the means. When covariance factors also vary, the divergence involves the full matrix-normal potential and additional coupling terms.

The authors identify the required computation as the matrix-variate analogue of an existing vector-case calculation but do not carry it out. The unresolved work includes both the closed form and the corresponding connection geometry.