Research On Several Types Of Constrained Split Quaternion Matrix Equations

The problem of constrained split quaternion matrix equation is to find the solution of the split quaternion matrix equation in a certain constrained matrix set.Different matrix equations or different constrained conditions will lead to different constrained split quaternion matrix equation problems.In this paper,we mainly investigate the direct method for solutions of some split quater-nion matrix equations.Firstly,we transform the split quaternion matrix equation into complex matrix equation or real matrix equation by the complex representation matrix or real represen-tation matrix of split quaternion matrix.Secondly,we discuss the consistent conditions and the expressions of solutions by vec-operator,Kronecker product and Moore-Penrose generalized inverse.Finally,we give the corresponding numerical algorithms and numerical examples.In the first chapter,we introduce the research background,purpose and mathematical sym-bols in this paper.In the second chapter,we mainly illustrate the preparatory knowledge used in this paper,including the properties of vec-operator,complex representation of split quaternion matrix,real representation of split quaternion matrix and their properties.In the third chapter,we study the consistent condition and the solution expressions of the anti-Hermite solution for the split quaternion matrix equations AX+XB=C and AXA~H+BY B~H=C.We give the numerical algorithm and numerical examples.In the forth chapter,we study the consistent condition and the solution expressions of the?-anti-bi-Hermitian solution for the split quaternion matrix equation AXB+CY D=E.We derive the explicit solutions and provide numerical algorithms and numerical examples to test these algorithms.In the fifth chapter,we use the real representation and the complex representation of split quaternion matrix to solve?-Hermitian solution for the split quaternion matrix equation AXB+CY D=E,respectively.We derive the consistent condition and the solution expressions,and provide corresponding numerical algorithms and numerical examples to test these algorithms.Finally,we compare the two methods.In the sixth chapter,we summarize our research results and present some next works in the future.