试题与答案

设A是n阶反对称矩阵, (Ⅰ) 证明:A可逆的必要条件是n为偶数;当n为奇数时,A

题型:问答题

题目:

设A是n阶反对称矩阵,
(Ⅰ) 证明:A可逆的必要条件是n为偶数;当n为奇数时,A*是对称矩阵;
(Ⅱ) 举一个4阶不可逆的反对称矩阵的例子;
(Ⅲ) 证明:如果λ是A的特征值,那么-λ也必是A的特征值.

答案:

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