# Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices

Special Matrices (2015)

- Volume: 3, Issue: 1, page 250-256, electronic only
- ISSN: 2300-7451

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topLuis Verde-Star. "Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices." Special Matrices 3.1 (2015): 250-256, electronic only. <http://eudml.org/doc/275834>.

@article{LuisVerde2015,

abstract = {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.},

author = {Luis Verde-Star},

journal = {Special Matrices},

keywords = {Triangular matrices; factorization; k-Hessenberg matrices; matrix inversion; triangular matrices; -Hessenberg matrices},

language = {eng},

number = {1},

pages = {250-256, electronic only},

title = {Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices},

url = {http://eudml.org/doc/275834},

volume = {3},

year = {2015},

}

TY - JOUR

AU - Luis Verde-Star

TI - Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices

JO - Special Matrices

PY - 2015

VL - 3

IS - 1

SP - 250

EP - 256, electronic only

AB - 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.

LA - eng

KW - Triangular matrices; factorization; k-Hessenberg matrices; matrix inversion; triangular matrices; -Hessenberg matrices

UR - http://eudml.org/doc/275834

ER -

## References

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- [2] Y. Ikebe, On inverses of Hessenberg matrices, Linear Algebra Appl., 24 (1979) 93–97. Zbl0397.15005
- [3] M. J. Piff, Inverses of banded and k-Hessenberg matrices, Linear Algebra Appl., 85 (1987) 9–15. Zbl0607.15004
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- [5] L. Verde-Star, Infinite triangular matrices, q-Pascal matrices, and determinantal representations, Linear Algebra Appl., 434 (2011) 307–318. Zbl1203.15021
- [6] L. Verde-Star, Divided differences and linearly recurrent sequences, Stud. Appl. Math. 95 (1995) 433–456. Zbl0843.65094
- [7] L. Verde-Star, Functions of matrices, Linear Algebra Appl., 406 (2005) 285–300.
- [8] Z. Xu, On inverses and generalized inverses of Hessenberg matrices, Linear Algebra Appl., 101 (1988) 167–180. Zbl0651.65030
- [9] T. Yamamoto, Y. Ikebe, Inversion of band matrices, Linear Algebra Appl., 24 (1979) 105–111. Zbl0408.15004

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