Question

设A为一正交矩阵 求证|A|=1或-1

Answer 1

正交阵就是(A^T)(A) = I 其中A^T表示A的转置,I 表示单位阵 两边取行列式|(A^T)(A)| = 1 |A^T| |A| =1 又因为|A^T| = |A| 所以|A|^2 = 1 |A| = 1或-1