Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
Luis Verde-Star
Special Matrices, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library
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We 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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:275834 
@article{bwmeta1.element.doi-10_1515_spma-2015-0025,
     author = {Luis Verde-Star},
     title = {Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices},
     journal = {Special Matrices},
     volume = {3},
     year = {2015},
     zbl = {1329.15073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0025}
}

Luis Verde-Star. Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0025/

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