Title:On the independence of linear and quadratic forms in matrix normal distribution and Wishart distribution

Speaker:Jiyuan Tao(Professor)

Time:  June 30,  2026, 10:30-12:00

Venue: Room 3A02, Building No. 37, Wushan Campus

Abstract: 

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.