13 Mar 2013
Undergraduate Lecture Series in Mathematics at University of Macau - Linear Algebra is not just Linear Algebra
澳大教授主講線性代數 展示數學獨有魅力

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.



講座中,鄭智文教授也分享了近期研究成果,他提到由澳大科技學院數學系黃錫榮教授和金小慶教授於二○○八年在《Operators and Matrices》期刊發表的論文《Proof of Böttcher and Wenzel's Conjecture》,兩教授於該論文證明了著名的“Bottcher and Wenzel猜想”,研究成果引起該領域其他學者的極大關注。鄭教授與其研究生對論文結果進行了詳細分析,並密切關注研究進展。隨後,鄭教授發現運用微積分的基本知識與技巧,能夠改進論文結果,並將之在《Linear Algebra and its Applications》期刊發表。鄭智文教授研究線性代數多年,主要從事矩陣理論的研究,包括:矩陣特徵值、奇異值及Hruwitz矩陣方程等。目前,鄭教授已在多份國際期刊發表了逾二十篇學術論文。