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

• Autorzy: Luis Verde-Star
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-08-18

zaakceptowano

2015-10-21

online

2015-11-06

Twórcy

autor

Luis Verde-Star

• Department of Mathematics, Universidad Autónoma Metropolitana, Iztapalapa,
  Apartado 55-534, México D. F. 09340, México

Bibliografia

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• [3] M. J. Piff, Inverses of banded and k-Hessenberg matrices, Linear Algebra Appl., 85 (1987) 9–15.
• [4] W. Shur, A simple closed form for triangular matrix powers, Electr. J. Linear Algebra, 22 (2011) 1000–1003.
• [5] L. Verde-Star, Infinite triangular matrices, q-Pascal matrices, and determinantal representations, Linear Algebra Appl., 434 (2011) 307–318.
• [6] L. Verde-Star, Divided differences and linearly recurrent sequences, Stud. Appl. Math. 95 (1995) 433–456.
• [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.
• [9] T. Yamamoto, Y. Ikebe, Inversion of band matrices, Linear Algebra Appl., 24 (1979) 105–111.

Identyfikatory

DOI

10.1515/spma-2015-0025