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.

澳門大學科技學院數學系本科生數學講座系列第四講“線性代數並不只是線性代數”日前於澳大何賢中心演講廳舉行,澳大數學系鄭智文教授與出席者分享線性代數的魅力,更向現場聽眾展示線性代數與其他學科的緊密聯繫,令聽眾從中獲益良多。

講座伊始,鄭教授首先分享了一篇關於線性代數研究的學術論文,從“矩陣特徵值”概念出發,帶領聽眾回顧線性代數的一些基本概念和有趣知識。同時,他展示了一個迄今仍未解決的有關線性代數的公開問題,更舉例指出線性代數的解法饒有趣味,給現場聽眾留下了深刻印象。

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。

澳大科技學院數學系本科生數學講座系列於上學期推出,邀請數學研究領域專家親臨澳大主講,讓澳大學生從不同角度出發,瞭解數學。該講座系列第五講將於下月中舉行,詳情將於稍後公佈,請密切留意。