Exact Score Vector and Hessian Matrix for Mixtures of Matrix‐Variate Normals

Closed-form expressions for the score vector and the Hessian matrix of the log-likelihood function are derived for mixtures ofmatrix-variate normal distributions. These results are obtained by exploiting properties of the trace operator and the Kronecker product, enabling fast and reliable computation of standard errors and eliminating the need for costly numerical differentiation. The advantages of the approach are highlighted through a comprehensive simulation study based on synthetic data under different scenarios.