The relationship between Kneser-Süss inequality and Minkowski inequality in mixed discriminant

Lu Zhu; Du Zou

doi:10.1117/12.2692901

23 August 2023 The relationship between Kneser-Süss inequality and Minkowski inequality in mixed discriminant

Lu Zhu, Du Zou

Proceedings Volume 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023); 1278413 (2023) https://doi.org/10.1117/12.2692901
Event: 2023 2nd International Conference on Applied Statistics, Computational Mathematics and Software Engineering (ASCMSE 2023), 2023, Kaifeng, China

Abstract

Brunn-Minkowski theory is an important theory of convex geometry. It is based on Minkowski addition of convex body, from which a series of concepts and inequalities in convex geometry are obtained. As we all know, these concepts and inequalities have been extended to matrices. Some of these inequalities are equivalent to each other in convex geometry, and similar results are obtained in mixed discriminant. This paper mainly discusses the relationship between Kneser-Süss inequality and Minkowski inequality in mixed discriminant, and proves that Kneser-Süss inequality and Minkowski inequality are equivalent in mixed discriminant.

Citation Download Citation

Lu Zhu and Du Zou "The relationship between Kneser-Süss inequality and Minkowski inequality in mixed discriminant", Proc. SPIE 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023), 1278413 (23 August 2023); https://doi.org/10.1117/12.2692901

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