Bézoutians of rational matrix functions, matrix equations and factorizations
Interconnections between Bézoutians of rational matrix functions, linear and quadratic equations and factorizations of rational matrix functions are studied. The Bézoutians are characterized as the angle operators generated by certain pairs of invariant subspaces. The factorizations \(F_I(\lambda)F(\lambda)= G_I(\lambda)G(\lambda)\), where \(F_I(\lambda)\), \(F(\lambda)\), \(G_I(\lambda)\), \(G(\lambda)\) are \(n\times n\) rational matrix functions, are described via the Bézoutian angle operators. Coprime factorizations and invertible solutions of Sylvester equations, different types of factorizations and doubly coprime minimal factorizations are discussed.
scientific article; zbMATH DE number 1419862
scientific article