注意到 ai=22o2ou=rwa@倒-会aa 1<≠k≤p 3ow-合2o-立au=(4a)-名a 1≤≠jsr 从而 E(Y'AYY'BY)=2tr(AB)+tr(A)tr(B). 最后 cov(Y'AY,YBY)=E(Y'AYY'BY)-E(YAY)E(Y'BY)=2tr(AB). ▣ Previous Next First Last Back Forward 7注意到 ∑∑ 1≤i̸=k≤p aiibkk = ∑p k=1 ∑p i=1 aiibkk − ∑p i=1 aiibii = tr(A)tr(B) − ∑p i=1 aiibii ∑∑ 1≤i̸=j≤p aij bij = ∑p j=1 ∑p i=1 aij bij − ∑p i=1 aiibii = tr(AB) − ∑p i=1 aiibii 从而 E(Y ′AY Y ′BY ) = 2tr(AB) + tr(A)tr(B). 最后 cov(Y ′AY, Y ′BY ) = E(Y ′AY Y ′BY )−E(Y ′AY )E(Y ′BY ) = 2tr(AB). Previous Next First Last Back Forward 7