On linear operators strongly preserving invariants of Boolean matrices

Title:

On linear operators strongly preserving invariants of Boolean matrices

Creator:

Chen, Yizhi and Zhao, Xianzhong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a687ab7f-1322-45b6-adfd-03269e085b25
uuid:a687ab7f-1322-45b6-adfd-03269e085b25

Subject:

linear operator, invariant, invertible matrix, regular matrix, and general Boolean algebra

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\mathbb {B}_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m,n}(\mathbb {B}_{k})$. If for any $A$ in $M_{m,n}(\mathbb {B}_{k})$ ($ M_{n}(\mathbb {B}_{k})$, respectively), $A$ is regular (invertible, respectively) if and only if $T(A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$. Meanwhile, noting that a general Boolean algebra $\mathbb {B}_{k}$ is isomorphic to a finite direct product of binary Boolean algebras, we also give some characterizations of linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$ from another point of view.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

169-186

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:1

Harvested from:

CDK

Metadata only:

false