西要毛子律技大学XIDIANUNIVERSITY即 α=Xe1 +X282 +..+X,en =(81,82,..8n)X,β= yie1 + y262 + ..+ yne, =(8,82...8n)Y,于是0(α) = 0(81,82....8n)X = (81,82....8n)AX,(β) = 0(61,62...en)Y =(61,62...6n)AY,又81,&2.,8n是标准正交基.: (o(α),β)=(AX)Y =(X'A')Y = X'AY= X'(AY) =(α,α(β)§9.6 对称矩阵的标准形 1 1 2 2 ... n n     = + + + y y y 1 1 2 2 ... n n 即     = + + + x x x  = (   ( ), ( ) ) AX Y = X AY ( ) 1 2 ( , ,..., ) , =    n X 1 2 ( , ,..., ) , =    n Y 于是 1 2 1 2 ( ) ( , ,..., ) ( , ,..., ) ,          = = n n X AX 1 2 1 2 ( ) ( , ,..., ) ( , ,..., ) ,          = = n n Y AY 又    1 2 , ,..., n 是标准正交基， = ( ) X A Y   = X AY  = (   , ( ))