Linear Preservers of Sub-Defect of Doubly Substochastics Matrices

Lei Cao; Ali Bayati Eshkaftaki; Selcuk Koyuncu

doi:10.1007/s00025-026-02645-0

Linear Preservers of Sub-Defect of Doubly Substochastics Matrices

Lei Cao
, Ali Bayati Eshkaftaki
, Selcuk Koyuncu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The sub-defect of a doubly substochastic matrix A, denoted by sd(A)=⌈n-sum(A)⌉, is defined as the minimum number of rows and columns required to be added to transform the doubly substochastic matrix into a doubly stochastic matrix. Here, n signifies the matrix size, and sum(A) represents the sum of all entries of A. In this paper, we provide the full characterization of all linear operators under which the sub-defect is preserved.

Original language	English
Article number	72
Journal	Results in Mathematics
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s00025-026-02645-0
State	Published - May 2026

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026.

ASJC Scopus Subject Areas

Mathematics (miscellaneous)
Applied Mathematics

Keywords

Doubly substochastic matrices
Linear operator
Sub-defect

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10.1007/s00025-026-02645-0

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abstract = "The sub-defect of a doubly substochastic matrix A, denoted by sd(A)=⌈n-sum(A)⌉, is defined as the minimum number of rows and columns required to be added to transform the doubly substochastic matrix into a doubly stochastic matrix. Here, n signifies the matrix size, and sum(A) represents the sum of all entries of A. In this paper, we provide the full characterization of all linear operators under which the sub-defect is preserved.",

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AU - Cao, Lei

AU - Eshkaftaki, Ali Bayati

AU - Koyuncu, Selcuk

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026.

PY - 2026/5

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N2 - The sub-defect of a doubly substochastic matrix A, denoted by sd(A)=⌈n-sum(A)⌉, is defined as the minimum number of rows and columns required to be added to transform the doubly substochastic matrix into a doubly stochastic matrix. Here, n signifies the matrix size, and sum(A) represents the sum of all entries of A. In this paper, we provide the full characterization of all linear operators under which the sub-defect is preserved.

AB - The sub-defect of a doubly substochastic matrix A, denoted by sd(A)=⌈n-sum(A)⌉, is defined as the minimum number of rows and columns required to be added to transform the doubly substochastic matrix into a doubly stochastic matrix. Here, n signifies the matrix size, and sum(A) represents the sum of all entries of A. In this paper, we provide the full characterization of all linear operators under which the sub-defect is preserved.

KW - Doubly substochastic matrices

KW - Linear operator

KW - Sub-defect

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UR - https://www.scopus.com/pages/publications/105033352818#tab=citedBy

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SN - 1422-6383

VL - 81

JO - Results in Mathematics

JF - Results in Mathematics

IS - 3

M1 - 72

ER -

Linear Preservers of Sub-Defect of Doubly Substochastics Matrices

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

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