求助：怎么证明n阶反对称矩阵行列式≥0 证明奇数级反对称阵的行列式为0
\u600e\u4e48\u8bc1\u660e\u53cd\u5bf9\u79f0\u77e9\u9635\u6309\u7167\u5b9a\u4e49\u6765\u5982\u679c\u4e00\u4e2a\u77e9\u9635\u7684\u8f6c\u7f6e\u4e0e\u8fd9\u4e2a\u77e9\u9635\u4e92\u4e3a\u76f8\u53cd\u6570\uff0c\u90a3\u4e48\u8fd9\u4e2a\u77e9\u9635\u5c31\u662f\u53cd\u5bf9\u79f0\u77e9\u9635\u3002
\u8bc1\u660e\uff1a\u6839\u636e\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u6027\u8d28\u6709\uff1a
AT=-A
|A|=|AT|=|-A|=\uff08-1\uff09n|A|=-|A|
\u7531\u4e8en\u4e3a\u5947\u6570
\u6240\u4ee5|A|=0
\u8bbeA\u4e3an\u7ef4\u65b9\u9635\uff0c\u82e5\u6709A'=-A\uff0c\u5219\u79f0\u77e9\u9635A\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002\u5bf9\u4e8e\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u4e3a\u96f6\uff0c\u800c\u4f4d\u4e8e\u4e3b\u5bf9\u89d2\u7ebf\u4e24\u4fa7\u5bf9\u79f0\u7684\u5143\u53cd\u53f7\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u884c\u5217\u5f0f\u53ef\u4ee5\u770b\u505a\u662f\u6709\u5411\u9762\u79ef\u6216\u4f53\u79ef\u7684\u6982\u5ff5\u5728\u4e00\u822c\u7684\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\u7684\u63a8\u5e7f\u3002\u6216\u8005\u8bf4\uff0c\u5728 n \u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\uff0c\u884c\u5217\u5f0f\u63cf\u8ff0\u7684\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u5bf9\u201c\u4f53\u79ef\u201d\u6240\u9020\u6210\u7684\u5f71\u54cd\u3002
\u53cd\u5bf9\u79f0\u77e9\u9635\u5177\u6709\u5f88\u591a\u826f\u597d\u7684\u6027\u8d28\uff0c\u5982\u82e5A\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5219A'\uff0c\u03bbA\u5747\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff1b\u82e5A,B\u5747\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5219A\u00b1B\u4e5f\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff1b\u8bbeA\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0cB\u4e3a\u5bf9\u79f0\u77e9\u9635\uff0c\u5219AB-BA\u4e3a\u5bf9\u79f0\u77e9\u9635\uff1b\u5947\u6570\u9636\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u884c\u5217\u5f0f\u5fc5\u4e3a0\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u53cd\u5bf9\u79f0\u77e9\u9635
题目应当是实数反对称阵行列式大于等于0。可以如图证明特征值都是0或纯虚数，所以行列式大于等于0。经济数学团队帮你解答，请及时采纳。谢谢！
绛旓細瀵圭О鐭╅樀鐨勫惈涔夋槸A涓庡叾杞疆鐭╅樀A'鐩哥瓑:A=A'鍙嶅绉扮煩闃鐨勫惈涔夋槸A涓庡叾杞疆鐭╅樀鐩稿姞涓0,鍗矨=-A'鍏充簬鐭╅樀鐨勮浆缃湁鑴辫。鍘熷垯鍗:(AB)'=B'A',(A+B)'=A'+B'鎴戜滑灏辩敤瀹氫箟,鍜岀涓夋潯鏉璇佹槑鏈 AB-BA鐨勮浆缃:(AB-BA)'=(AB)'-(BA)'=B'A'-A'B'[浠ヤ笂涓鸿劚琛ｅ師鍒欏緱鍒扮殑]=(-BA)-(A(-B)...
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