The 6th International Conference on Matrix Analysis and Its Applications (ICMAA 2017) was held in Danang, a beautiful city in Central Vietnam, June 15-18, 2017. The previous conferences were held in China (Beijing, Hangzhou), United States (Nova Southeastern University), and Turkey (Selcuk University, Konya). Former keynote speakers are Roger Horn, Richard Brualdi, Chi-Kwong Li, Steve Kirkland, Alexander A. Klyachko (ILAS guest speaker), and Shmuel Friedland.
This meeting aims to stimulate research and interaction of mathematicians in all aspects of linear and multilinear algebra, matrix analysis, graph theory, and their applications and to provide an opportunity for researchers to exchange ideas and developments on these subjects.
ICMAA 2017 was supported by Duy Tan University and ILAS. We welcomed 70 participants from 17 countries to Danang. The keynote speaker of the ICMAA 2017 was Dr. Man-Duen Choi. Three invited talks were also given by famous mathematicians in matrix theory, professors Tsuyoshi Ando, Abraham Berman and Richard Brualdi.
The early registration started on June 15. All talks were on 16-17 June at the main campus of Duy Tan University. On June 18, participants visited the famous Linh Ung Pagoda and Marble Mountains in Danang city. Dr Choi opened the conference with an interesting keynote lecture on tensor products of complex matrices and his mathematical journey. He explained the connection between tensor products and quantum entanglement and the Principle of Locality in quantum information theory. We also welcomed 46 contributed talks on different topics such as: combinatorics, numerical algebra, matrix equations, graph theory, operator algebra theory, non-commutative algebraic geometry etc.
ICMAA 2017 was a very successful event. At the same time, it was an excellent introduction of many topics in matrix analysis and its applications to the Vietnamese math community. The journal Acta Mathematica Vietnamica will publish a special issue on Matrix Analysis and Its Applications in 2018. All are welcome to submit papers for this issue.
The matrix Heron mean is quite interesting object. It is an interpolation between the arithmetic and the geometric means. For numbers, the Heron mean is the volume of the frustum with bases a, b and height 1.
In the third paper with my friends Jose and Raluca at the University of North Florida, we compare norms of the non-Kubo-Ando extensions of the Heron mean and the Heinz mean. Surprisingly, we started from a special case of Bhatia’s inequality for numbers, but for matrices it turns out that our result covers Bhatia’s and Kaur-Singh’s results.
In difference to the well-known interpolation of the matrix arithmetic-geometric mean inequality with the Heinz mean, a similar interpolation with the Heron mean is not true in general.
Here is a preprint which will be submitted very soon: The matrix Heron mean and interpolation
The second joint paper with friends at the University of North Florida was accepted to publish in Linear Algebra and Its Applications. In this short note (P_t_Q_t), we prove a conjecture due to Bhatia, Lim, and Yamazaki on the matrix power means.
Here is the link to the paper in Linear Algebra and Its Applications:
A new paper with new friends from the University of North Florida is online now in Linear Algebra and Its Applications.
The following picture for positive numbers is obvious. And it is surprising that hundreds of papers were published in good journals to with purpose to understand the same picture for positive matrices.
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The paper with Prof. Tin-Yau Tam and A. Sima is online at:
In this project, A. Sima partially worked under my supervision.