证明.由于Y'AY=∑aYy,Y'BY=∑e betYeY,以及 3,i=j=k=l 1, i=j≠k=l E(YYjYY)= i=k≠j=l i=l≠k=j 0, 其他 于是 arym 1≤≠k≤p +∑∑ab+∑∑akbi 1≤≠j≤p 1≤≠k≤r = 3∑aib:+∑∑abk+2∑∑abg i=1 1≤i≠k≤p 1≤≠j≤p Previous Next First Last Back Forward 6证明. 由于 Y ′AY = ∑ i,j aijYiYj , Y ′BY = ∑ k,l bklYkYl, 以及 E(YiYjYkYl) =    3, i = j = k = l 1, i = j ̸= k = l i = k ̸= j = l i = l ̸= k = j 0, 其他 于是 E(Y ′AY Y ′BY ) = 3∑p i=1 aiibii + ∑∑ 1≤i̸=k≤p aiibkk + ∑∑ 1≤i̸=j≤p aij bij + ∑∑ 1≤i̸=k≤p aikbki = 3∑p i=1 aiibii + ∑∑ 1≤i̸=k≤p aiibkk + 2 ∑∑ 1≤i̸=j≤p aij bij Previous Next First Last Back Forward 6