An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...

In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation AXB + CXHD = F. When the matrix equation is consistent over reflexive matrix X, a reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors. By the proposed iterative algorithm, the least Frobenius norm reflexive solution of the matrix equation can be d...

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another ...