报告主题：对偶矩阵的分解及其应用

主讲人：魏益民教授（复旦大学）

主持人：尹国建

时 间：2024年3月04日周一10:30

地 点：致知楼706

嘉宾简介：

担任国际学术期刊Computational and Applied Mathematics, Journal of Applied Mathematics and Computing, FILOMAT,和Communications in Mathematical Research,《高校计算数学学报》的编委。在国际学术期刊Math. Comput., SIAM J. Sci. Comput.,SIAM J. Numer Anal., SIAM J. Matrix Anal. Appl., J. Sci. Comput., IEEE Trans. Auto. Control, IEEE Trans.Neural Network Learn. System, Neurocomputing和Neural Computation等发表论文150余篇;在EDP Science, Elsevier, Springer, World Scientific和科学出版社等出版英语专著5本。5次入选爱思唯尔“中国高被引学者”榜单. Google学术引用8900余次，H指数48。

报告摘要：

Matrix Decompositions in dual number algebra, a hypercomplex system, have been applied to several fields. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves using the singular value decomposition of dual matrices. We present the compact dual singular value decomposition (CDSVD), UTV and QR decompositions of dual complex matrices with explicit expressions as well as a necessary and sufficient condition for its existence. We apply these approaches to the large-scale brain fMRI data, identify three kinds of traveling waves, andfurther validate the consistency between our analytical results and the current knowledge of cerebral cortex function.