讲座题目🧛🏽：Nuclear Norm and Spectral Norm of Tensor Product 主讲人：祁力群 教授 主持人🩳：潘建瑜 教授 开始时间：2019-10-11 14:00:00 讲座地址🫁：闵行数学楼102报告厅 主办单位：数学科学学院
报告人简介： 祁力群教授是国际运筹学和最优化领域的领军人物之一，他1968年毕业于清华大学🤱🏽🤵🏿，1981年在美国威斯康星大学取得硕士，1984年在美国威斯康星大学获得博士学位🫃🏻。祁力群教授先后任教于清华大学、澳大利亚新南威尔士大学、香港城市大学等，现为香港理工大学应用数学系讲座教授，香港科学基金委成员🎇，担任10个国际杂志编委，发表学术论文超过300篇，是ISI高被引科学家之一，曾荣获中国运筹学会科学技术奖一等奖🪈👨🏿🍼，香港理工大学校长奖等。在最近十多年里，祁力群教授在张量研究方面做出了一系列的开创性工作，并分别在SIAM和Springer出版了两本论著“Tensor Analysis: Spectral Theory and Special Tensors”（2017）和“Tensor Eigenvalues and Their Applications”（2018）。 报告内容： We show that the nuclear norm of the tensor product of two tensors is not greater than the product of the nuclear norms of these two tensors. As an application, we give lower bounds for the nuclear norm of an arbitrary tensor. We show that the spectral norm of the tensor product of two tensors is not greater than the product of the spectral norm of one tensor, and the nuclear norm of another tensor. By this result, we present an alternative formula for the spectral norm of a tensor, and give some lower bounds for the product of the nuclear norm and the spectral norm of an arbitrary tensor. The first result also shows that the nuclear norm of the square matrix is a matrix norm. We then extend the concept of matrix norm to tensor norm. A real function defined for all real tensors is called a tensor norm if it is a norm for any tensor space with fixed dimensions, and the norm of the tensor product of two tensors is always not greater than the product of the norms of these two tensors. We show that the 1-norm, the Frobenius norm and the nuclear norm of tensors are tensor norms but the infinity norm and the spectral norm of tensors are not tensor norms. |
