A Solution For Solving A System Of Quasi-Hessenberg Equations

Hessenberg matrix, quasi-Hessenberg matrix, system of Hessenberg equationsand system of quasi-Hessenberg equations are very important in numerical algebra.In calculation of eigenvalue of matrix, solution of system of Hessenberg equationsplay a very actual role. On the other hand, application of Hessenberg matrix andsystem of Hessenberg equations is very universal. For example, generalized Hes-senberg method, incompleted generalized Hessenberg method, eigenvalue of unde-fective matrix, incompleted orthogonal method. Therefore, research on Hessenbergmatrix, quasi-Hessenberg matrix, system of Hessenberg equations and system ofquasi-Hessenberg equations is very important.There are many useful properties and theorems about Hessenberg matrix andsystem of Hessenberg equations in numerical algebra. These conclusions containinverse matrix of irreducible block Hessenberg matrix, relations of Hessenberg matrixand Toeplitz matrix, solution of system of Hessenberg equations and system of quasi-Hessenberg equations.In this paper, we simply discussed :(1)some properties and application of Hessenberg matrix and system of Hes-senberg equations,(2)solution of system of Hessenberg equations and system of quasi-Hessenbergequations.