Question

A为实对称可逆矩阵,把二次型f=xTAx化为f=yTA^(-1)y的线性变换是x=____ y.

Answer 1

令 X=A^-1Y

因为A是实对称矩阵

所以 (A^-1)^T = (A^T)^-1 = A^-1.

则 f = X^TAX = Y^T (A^-1)^T A A^-1 Y = Y^TA^-1Y