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Some New Elements of the Elliptic Brunn-Minkowski Theory

Some New Elements of the Elliptic Brunn-Minkowski Theory

Original Research ArticleNov 12, 2018Vol. 5 No. 1 (2005)

Abstract

In this paper, we present various matrix analog of notions and inequalities in convex geometry. We employ the well known notion of mixed determinant - and analog of the notion of mixed volume in convex geometry, and introduce the matrix version of Blaschke summation – an analog of the notion of Blaschke summation for convex bodies. With these notions we then can develop some matrix analogs of the convex geometry. In this paper, we also present one new inequality analog – the matrix version of Kneser-Süss inequality.

Keywords: Minkowski inequality, Brunn-Minkowski inequality, Kneser-Süss inequality, Minkowski’s determinant inequality, Blaschke summation, Matrix Blaschke summation, Mixed determinant, Matrix Kneser-Süss inequality

Corresponding author: E-mail: ppranaya@duke.poly.edu

How to Cite

Pranayanuntana, P. . (2018). Some New Elements of the Elliptic Brunn-Minkowski Theory. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 172-180.

References

  • Schneider, R., 1993. Conver Bodies: The Brunn-Minkowski Theory. Cambridge University Press, New York.
  • Lutwak, E., April 1986. Volume of mixed bodies. Transactions of The American Mathematical Society, 294, 2: 487-500.
  • Horn, R. A. and Johnson, C. R., 1985. Matrix Analysis. Cambridge University Press, New York.
  • Marcus, M. and Minc, H., 1964 A Survey of Matrix Theory and Matrix Inequalities. Dover Publications, New York.
  • Prasolov, V. V., 1994. Problems and Theorems in Linear Algebra, volume 134. American Mathematical Society, United States.

Author Information

Poramate Pranayanuntana

Department of Control Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand

About this Article

Journal

Vol. 5 No. 1 (2005)

Type of Manuscript

Original Research Article

Keywords

Minkowski inequality, Brunn-Minkowski inequality, Kneser-Süss inequality, Minkowski’s determinant inequality, Blaschke summation, Matrix Blaschke summation, Mixed determinant, Matrix Kneser-Süss inequality

Published

12 November 2018