设A为mˉ阶非奇异实矩阵,记A=[a12a2…,an,其中 )(j=1,2,…,n) Exb,a,/,. b2=a-a, b 6=an al (a2a4)(a2a)(a12a1 0 a.a ila h⊥b2取b2=b2则=临=1.(,b2)=0 般地取b=4-∑(a2b为,b=b/(k=2,3…n) 则向量组bb2…,b正交,且 1(k=1,2,…n) 即ak=(a,b)b+…+(a4b1-)b-+|11 2 1 2 ' 2 1 1 1 1 2 2 2 1 1 2 1 2 1 2 1 2 1 2 1 1 1 ' 2 1 1 2 1 1 1 1 1 1 ' ' ' 1 2 2 2 2 1 2 [ , , , ], ( , , , ) ( 1, 2, , ). , / . , , , , , , 0 , , / , 1 n T j j j nj A n A a a a a a a a j n a a b a a b a a b b a a a a a a a a a a a a a b b a a a a a a b b b b b b b = = = = = − = − = −  = − =  ⊥ = = = 设 为 阶非奇异实矩阵，记 其中 取 取 则 1 2 1 ' ' ' 1 1 2 ' 1 1 1 1 , , 0. , , / ( 2,3, ) , , , 1 ( 1, 2, ) , , k k k k i i k k k i n k k k k k k k k b b b a a b b b b b k n b b b b k n a a b b a b b b b − = − − = = − = = = = = + + + 一般地取  则向量组 正交，且 即