Inverses of regular Hessenberg matrices
نویسندگان
چکیده
A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of the inverse matrix. As an application of current interest in the theory of orthogonal polynomials on the complex plane, the resolvent matrix associated to a finite Hessenberg matrix in standard form is calculated. The results are illustrated with two examples on the unit disk.
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