偶数阶反对称行列式的正负 偶数阶反对称行列式取值范围
\u5076\u6570\u9636\u53cd\u5bf9\u79f0\u77e9\u9635\u884c\u5217\u5f0f\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u5408\u540c\u6807\u51c6\u578b\u662fdiag{D,D,...,D,0,...,0}\uff0c\u5176\u4e2d
D=
0 1
-1 0
\u5f53\u7136\u4e5f\u53ef\u4ee5\u770b\u7279\u5f81\u503c\uff0c\u5b9e\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u7279\u5f81\u503c\u90fd\u5728\u865a\u8f74\u4e0a\uff0c\u4e14\u6210\u5bf9\u51fa\u73b0
\u4e0d\u662f, \u81f3\u5c112\u9636\u7684\u4e0d\u662f
0 x
-x 0
\u884c\u5217\u5f0f\u7b49\u4e8e x^2
\u5728\u5b9e\u6570\u5185\u7684\u53d6\u503c\u8303\u56f4\u662f 0 \u5230 \u65e0\u7a77\u5927
证明的话，他所有的特征值非零的话一定是纯虚数，结果显然。
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绛旓細鍙嶅绉扮煩闃电殑鎬ц川鏈夛細涓嶅瓨鍦ㄥ鏁扮骇鐨勫彲閫嗗弽瀵圭О鐭╅樀锛屽弽瀵圭О鐭╅樀鐨勪富瀵硅鍏冪礌鍏ㄤ负闆讹紝鍙嶅绉扮煩闃电殑绉╀负鍋舵暟锛屽弽瀵圭О鐭╅樀鐨勭壒寰佸兼垚瀵瑰嚭鐜(瀹鍙嶅绉扮殑鐗瑰緛鍊间负0鎴栫函铏氭暟)锛屽弽瀵圭О鐭╅樀鐨琛屽垪寮涓洪潪璐熷疄鏁般傚弽瀵圭О鐭╅樀锛氳A涓簄缁存柟闃碉紝鑻ユ湁A'=-A锛屽垯绉扮煩闃礎涓哄弽瀵圭О鐭╅樀銆傚浜庡弽瀵圭О鐭╅樀锛屽畠鐨勪富瀵硅...
绛旓細濡傛灉鍙嶅绉鐭╅樀 A 鏄鏁伴樁锛岄偅涔 |A| = 0锛屾槸涓畬鍏ㄥ钩鏂规暟銆傚鏋滄槸鍋舵暟闃锛屽綊绾冲亣璁 <=2k 鐨勫弽瀵圭О鐭╅樀 |A| = 瀹屽叏骞虫柟鏁帮紝鐜拌瘉 n=2k+2 闃剁殑銆傚弽瀵圭О鐭╅樀鐨勫瑙掑厓绱犻兘鏄0銆傚鏋滅1琛屽厓绱犲叏鏄0锛岄偅涔 |A| = 0 鏄釜瀹屽叏骞虫柟鏁般傚鏋滅1琛屾湁1涓厓绱犱笉鏄0锛屼笉濡ㄨ a_{1,2} 涓嶆槸...
绛旓細璇佹槑: 璁続鏄鍋舵暟闃跺弽瀵圭О鐭╅樀, 鍒橝= 0 a12 ... a1n -a12 0 ... a2n ... ...-a1n -a2n ... 0 姣忎釜鏁伴兘鍔犱笂k鐨琛屽垪寮 璁颁负 |A(k)| = k a12+k ... a1n+k -a12+k k ... a2n+k ... ...-a1n+k -a2n+k ... k 鍔犺竟 1 k k ...
