block hessenberg matrices
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2021 ◽  
Vol 71 (2) ◽  
pp. 341-358
Author(s):  
Edinson Fuentes ◽  
Luis E. Garza

Abstract In this contribution, we study properties of block Hessenberg matrices associated with matrix orthonormal polynomials on the unit circle. We also consider the Uvarov and Christoffel spectral matrix transformations of the orthogonality measure, and obtain some relations between the associated Hessenberg matrices.


2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Luis Verde-Star

AbstractWe use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its nonzero entries in the k-th column,where 1 ≤ k ≤ n.


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