线性代数计算题 求一个正交变换,将下列二次型化为标准f（X1,X2,X3)=2X1^2+2X2^+2X3^2+2X1X2+2X1X3+2X2X3
问题描述：
线性代数计算题 求一个正交变换,将下列二次型化为标准f（X1,X2,X3)=2X1^2+2X2^+2X3^2+2X1X2+2X1X3+2X2X3
答
f(x1,x2,x3) = (x1+x2)^2 + (x2+x3)^2 + (x1+x3)^2设y1 = x1 + x2y2 = x2 + x3y3 = x1 + x3然后用y表示x就行x1 = 1/2 （y3-y2 +y1）x2 = 1/2 (y1-y3+y2)x3 = 1/2 (y1-y2+y3)然后写成X = P YP就是所求正交变换...