Constructive Algorithm to Vectorize P ⊗ P Product for Symmetric Matrix P - Glushchenko, A. I.; Lastochkin, K. A. (Computational mathematics and mathematical physics, 2023)
A constructive algorithm to compute elimination and duplication matrices for the operation of vectorization when is proposed. The matrix , obtained according to such algorithm, allows one to form a vector that contains only unique elements of the mentioned Kronecker product. In its turn, the matrix is for the inverse transformation. A software implementation of the procedure to compute the matrices and is developed. On the basis of the mentioned results, a new operation is defined for in case and its properties are studied. The difference and advantages of the developed operation in comparison with the known ones and ( ) in case of vectorization of when are demonstrated. Using parameterization of the algebraic Riccati equation as an example, the efficiency of the operation to reduce overparameterization of the unknown parameter identification problem is shown.