»ã±¨±êÌâ (Title)£ºOn the independence of linear and quadratic forms in matrix normal distribution and Wishart distribution£¨¾ØÕóÕý̬ɢ²¼ºÍWishartÉ¢²¼ÖÐÏßÐÔ´ó¾ÖºÍ¶þ´Î´ó¾ÖµÄ¶ÀÁ¢ÐÔ£©

»ã±¨ÈË (Speaker)£ºJiyuan Tao ½ÌÊÚ£¨ÂíÀïÀ¼ÂåÔ¼À­´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê6ÔÂ13ÈÕ£¨ÖÜÎ壩9:30-10:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÍõÇäÎÄ ½ÌÊÚ

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»ã±¨ÌáÒª£ºIt is well-known that the Craig-Sakamoto theorem establishes the independence of two quadratic forms in normal variates. Replacing the random normal vectors by the random normal matrices and Wishart variates, in this talk, we present interconnections between the independence of linear forms, quadratic forms, trace forms in matrix normal distribution and Wishart distribution. We show that the Craig-Sakamoto theorem still establishes the independence of two quadratic forms in matrix normal distribution, but it does not establish the independence of two quadratic forms in Wishart variates.»ã±¨È˼ò½é£ºJiyuan Tao received his Ph.D. in Applied Mathematics, University of Maryland, Baltimore County, U.S.A. in 2004. He is a full professor in the department of mathematics and statistics, Loyola University Maryland, U.S.A. He was awarded ``Distinguished Scholar of the Year, Loyola University Maryland (2018)''. His research field is in optimization and focuses on complementarity problems over symmetric cones and Euclidean Jordan algebras. He has been published in numerous prestigious peer-reviewed journals including Mathematical Programming and Mathematical Operations Research which are top-tier journals in the optimization community, and Linear Algebra and its Applications and Linear and Multilinear Algebra which are top-tier journals in the linear algebra society. He was an invited speaker in various international meetings. He has been a reviewer for several reputed journals like Mathematical Programming, SIAM Optimization, Journal of Linear Algebra and its Applications, Journal of Optimization Theory and Applications.