报告题目 (Title)：On the independence of linear and quadratic forms in matrix normal distribution and Wishart distribution（矩阵正态分布和Wishart分布中线性形式和二次形式的独立性）
报告人 (Speaker)： Jiyuan Tao 教授（马里兰洛约拉大学）
报告时间 (Time)：2025年 6 月13日 (周五) 9：30-10：30
报告地点 (Place)：校本部F309
邀请人(Inviter)：王卿文
报告摘要：It 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.