即 α= X,e1 +X262 + ... + X,, =(61,82..en)X,β= yiei + y2e2 +... + ynen =(e1,e2,...en)Y,于是0(α) = 0(81,82....8n)X = (81,82,...8,)AX,(β) =o(81,62....8n)Y =(81,62....8n)AY,又81,82..…,8n是标准正交基，.. (α(α),β)=(AX)Y =(X'A)Y = X'AY= X'(AY) =(α,α(β))$9.6对称矩阵的标准形K§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  = (   , ( ))