ScholarLens Back to search
2010•Harbin Gongcheng Daxue Xuebao/Journal of Harbin Engineering UniversityRequires access

Involutiveness of a linear combination of a class matrix

Li Na

Open publisher page 0 citations

Abstract

Let A1 and A2 be nonzero complex matrices.Denote a linear combination of the two matrices by A=c1A1+c2A2,where c1,c2∈C are nonzero scalars.The study of idemopotency,tripotency and involution of linear combinations of matrices has important applications in many fields.In this paper,by use of the standard form of a tripotent matrix,we characterized the sufficient and necessary conditions for the involutive combination of A,with A1,A2 as idempotent and tripotent matrices,respectively,without the assumption that A1A2=A2A1.

About this research paper

What this paper is about

Let A1 and A2 be nonzero complex matrices.Denote a linear combination of the two matrices by A=c1A1+c2A2,where c1,c2∈C are nonzero scalars.The study of idemopotency,tripotency and involution of linear combinations of matrices has important applications in many fields.In this paper,by use of the standard form of a tripotent matrix,we characterized the sufficient and necessary conditions for the involutive combination of A,with A1,A2 as idempotent and tripotent matrices,respectively,without the assumption that A1A2=A2A1.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let A1 and A2 be nonzero complex matrices.Denote a linear combination of the two matrices by A=c1A1+c2A2,where c1,c2∈C are nonzero scalars.The study of idemopotency,tripotency and involution of linear combinations of matrices has important applications in many fields.In this paper,by use of the standard form of a tripotent matrix,we characterized the sufficient and necessary conditions for the involutive combination of A,with A1,A2 as idempotent and tripotent matrices,respectively,without the assumption that A1A2=A2A1.

Key concepts: Mathematics, Complex matrix, Idempotence, Matrix (chemical analysis), Class (philosophy), Pure mathematics, Matrix analysis, Algebra over a field

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Involutiveness of a linear combination of a class matrix — Research Paper | ScholarLens