ScholarLens Back to search
2009•Unpublished venueRequires access

The inverses of the combinations of two idempotent matrices

Kezheng Zuo

Open publisher page 0 citations

Abstract

The paper researches the inverses of combinations of two idempotent matrices P±Q,I-PQ,aP+bQ - cPQ - dQP(where P,Q are two idempotent matrices).It first proves a rank equality of the combinations of two idempotent matrices aP +bQ - cPQ (where a≠0,b≠0,P,Q are two idempotent matrices)by using elementary transformations of block matrices.Secondly,the explicit expressions of some invertible combinations P±Q,I-PQ,aP + bQ-cPQ-dQP(where P,Q are idempotent matrices) are obtained by using the properties of the invertibility of P-Q and projectors when P - Q is invertible.Those expressions describe some features of the combinations of two idempotent matrices.

About this research paper

What this paper is about

The paper researches the inverses of combinations of two idempotent matrices P±Q,I-PQ,aP+bQ - cPQ - dQP(where P,Q are two idempotent matrices).It first proves a rank equality of the combinations of two idempotent matrices aP +bQ - cPQ (where a≠0,b≠0,P,Q are two idempotent matrices)by using elementary transformations of block matrices.Secondly,the explicit expressions of some invertible combinations P±Q,I-PQ,aP + bQ-cPQ-dQP(where P,Q are idempotent matrices) are obtained by using the properties of the invertibility of P-Q and projectors when P - Q is invertible.Those expressions describe some features of the combinations of two idempotent matrices.

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

The paper researches the inverses of combinations of two idempotent matrices P±Q,I-PQ,aP+bQ - cPQ - dQP(where P,Q are two idempotent matrices).It first proves a rank equality of the combinations of two idempotent matrices aP +bQ - cPQ (where a≠0,b≠0,P,Q are two idempotent matrices)by using elementary transformations of block matrices.Secondly,the explicit expressions of some invertible combinations P±Q,I-PQ,aP + bQ-cPQ-dQP(where P,Q are idempotent matrices) are obtained by using the properties of the invertibility of P-Q and projectors when P - Q is invertible.Those expressions describe some features of the combinations of two idempotent matrices.

Key concepts: Idempotent matrix, Idempotence, Invertible matrix, Mathematics, Rank (graph theory), Combinatorics, Block (permutation group theory), Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The inverses of the combinations of two idempotent matrices — Research Paper | ScholarLens