The fourth lecture of Undergraduate Lecture Series in Mathematics held by Department of Mathematics of Faculty of Science and Technology has held on 6 March 2013 in Ho Yin Convention Centre HG02. Prof. Che-Man Cheng, Associate Professor of Department of Mathematics, was invited as speaker.

Prof. Cheng began the lecture by sharing a research paper of linear algebra, and revisited some of the basic concepts and interesting knowledge in linear algebra. Later, Prof. Cheng demonstrated the charm of the linear algebra by an open problem which only consisted of the elementary concepts, and there is no perfect solution for this problem until now. The audiences are deeply impressed by the example. 

Prof. Cheng also introduced his recent research, and the paper “Proof of Böttcher and Wenzel’s Conjecture” in the journal “Operators and Matrics” by Prof. Seak-Weng Vong and Prof. Xiao-Qing Jin of Department of Mathematics. In this paper, Prof. Vong and Prof. Jin proved the famous Böttcher and Wenzel’s Conjecture. This result highly motivated a series of related works by other researchers. After detail analysis on the result of the paper, and close attention to the progress of the related research, Prof. Cheng and his graduate students found that the result in the paper can be improved with some elementary skills in Calculus. This work has been published on the journal “Linear Algebra and its Applications” by Prof. Cheng’s group. With this example, Prof. Cheng successfully shown that linear algebra had very close relation with other discipline. The audience benefited a lot from research experience of Prof. Cheng.

Prof. Cheng focuses on the research of matrix theory, including numerical ranges, eigenvalues and singular values, and Hurwitz matrix equations. He has published more than 20 papers in the international journals such as “Linear Algebra and its Applications”.

The fifth lecture of Undergraduate Lecture Series in Mathematics at UM will be launched in April. All are welcome to join the lecture.


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