设n阶方阵A满足下面三个条件：A的转置等于A；A的2次方等于A；A的行列式不等于0.证明：A是正定矩阵.

根据已知条件有：A^T = A (A^T表示A的转置),A^2 = A * A = A^T * A=A.对任意的向量X,有X^T * A * X = X^T * A^2 * X = X^T * A * A * X = X^T * A^T * A * X = (AX)^T * (AX),令AX = Y = (y1,...,yn),则：X^T * A * ...