Linear maps preserving the Cullis' determinant. II

2025/12/15 by Alexander Guterman, Guterman, Alexander, A. V. Yurkov +1 · 1 citation
Computer Science · Mathematics · #15A15 #15A86 #47B49 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2512.13445

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging to an arbitrary ground field which is large enough. In this part we solve the linear preserver problem for the Cullis' determinant defined on the spaces of matrices of size n× k with k ≥ 4, n ≥ k + 2 and n + k is odd. In comparison with the case when n + k is even, in this case linear maps preserving the Cullis' determinant could be singular and are represented as a sum of two linear maps: first is two-sided matrix multiplication and second is any linear map whose image consists of matrices, all rows of which are equal.

Citations

• On the linear preservers of Schur matrix functionals
• Discriminant preserving linear maps

Cited by

• Linear varieties and matroids with applications to the Cullis' determinant

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