Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
View through CrossRef
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.
Title: Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
Description:
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.
Related Results
Inner-gMP and gMP-inner inverses
Inner-gMP and gMP-inner inverses
Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called i...
Nonsparse companion Hessenberg matrices
Nonsparse companion Hessenberg matrices
In recent years, there has been a growing interest in companion matrices. Sparse companion matrices are well known: every sparse companion matrix is equivalent to a Hessenberg matr...
Inner-Φ-GCEP and Φ-GCEP-inner inverses
Inner-Φ-GCEP and Φ-GCEP-inner inverses
Inspired by the concepts of ?-GCEP and ?-*GCEP inverses as generalizations of the gMP, *gMP and MP inverse, the aim of this paper is to extend notions of inner-gMP, gMP-inner, inne...
Quaternion MPCEP, CEPMP, and MPCEPMP Generalized Inverses
Quaternion MPCEP, CEPMP, and MPCEPMP Generalized Inverses
A generalized inverse of a matrix is an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses exist for an arbitrary matrix and coincid...
When Does a Dual Matrix Have a Dual Generalized Inverse?
When Does a Dual Matrix Have a Dual Generalized Inverse?
This paper deals with the existence of various types of dual generalized inverses of dual matrices. New and foundational results on the necessary and sufficient conditions for vari...
Implementasi Pembelajaran IPS Sebagai Penguatan Pendidikan Karakter di Sekolah Dasar
Implementasi Pembelajaran IPS Sebagai Penguatan Pendidikan Karakter di Sekolah Dasar
This study aims to analyze the implementation of social studies learning as strengthening character education in elementary schools. The research method used is a qualitative descr...
METODE FULL ORTHOGONALIZATION UNTUK MENYELESAIKAN SISTEM PERSAMAAN LINEAR
METODE FULL ORTHOGONALIZATION UNTUK MENYELESAIKAN SISTEM PERSAMAAN LINEAR
Sistem persamaan linear dapat diselesaikan dengan metode langsung dan metode iteratif. Salah satu metode iteratif untuk menyelesaikan sistem persamaan linear yaitu metode Full Orth...
Some properties of Max-Plus Algebra and generalized inverses on 2x2 matrices integers modulo 3
Some properties of Max-Plus Algebra and generalized inverses on 2x2 matrices integers modulo 3
Abstract
The properties of Max Plus Algebra can be applied to the matrix. Furthermore, the generalized inverses in a matrix can also be related to this algebra. This...