二次型的矩阵 A =
1 1 0
1 2 2
0 2 4
分块矩阵 (上下放置)
A
E
=
1 1 0
1 2 2
0 2 4
1 0 0
0 1 0
0 0 1
r2-r1,c2-c1
1 0 0
0 1 2
0 2 4
1 -1 0
0 1 0
0 0 1
r3-2r2,c3-2c2
1 0 0
0 1 0
0 0 0
1 -1 2
0 1 -2
0 0 1
令 P=
1 -1 2
0 1 -2
0 0 1
X=PY,f = y1^2+y2^2.
验证:P^TAP = diag(1,1,0).