什么是反对称矩阵?详细回答 什么是反对称矩阵

\u4ec0\u4e48\u662f\u53cd\u5bf9\u79f0\u77e9\u9635\uff1f\u8be6\u7ec6\u56de\u7b54

\u5bf9\u79f0\u77e9\u9635
\u5b9a\u4e49\u662f
A=A\u7684
\u8f6c\u7f6e
\u53cd\u5bf9\u79f0\u77e9\u9635
\u5b9a\u4e49\u662f
A=
-
A\u7684\u8f6c\u7f6e
\u8f6c\u7f6e\u4f60\u77e5\u9053\u5427\uff1f
\u4e00\u4e2a\u77e9\u9635\u884c\u5217\u4e92\u6362\u5c31\u53d8\u6210\u5b83\u7684
\u8f6c\u7f6e\u77e9\u9635
\u6216\u8005\u8bf4
,\u53cd\u5bf9\u79f0\u77e9\u9635\u662f\u8fd9\u6837\u4e00\u4e2a\u77e9\u9635
\u5b83\u7684\u7b2cI\u884c\u548c\u7b2cI\u5217
\u5404\u6570
\u7edd\u5bf9\u503c\u76f8\u7b49\uff0c\u7b26\u53f7\u76f8\u53cd

\u8bbe \uff0c\u82e5\u5176\u5143\u7d20\u6ee1\u8db3 \uff0c\u5219\u79f0A\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002
\u4f8b\u5b50\uff1aA=[0 1][ -1 0]\u662f\u4e2a\u4e8c\u9636\u53cd\u5bf9\u79f0\u77e9\u9635\u3002
\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
\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\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u7279\u5f81\u503c\u662f0\u6216\u7eaf\u865a\u6570\uff0c\u5e76\u4e14\u5bf9\u5e94\u4e8e\u7eaf\u865a\u6570\u7684\u7279\u5f81\u5411\u91cf\u7684\u5b9e\u90e8\u548c\u865a\u90e8\u5f62\u6210\u7684\u5b9e\u5411\u91cf\u7b49\u957f\u4e14\u4e92\u76f8\u6b63\u4ea4\u3002

\u6269\u5c55\u8d44\u6599\uff1a
\u57fa\u672c\u6027\u8d28

\u6027\u8d281\uff1a
\u8bbeA,B\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5219A\u00b1B\u4ecd\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002
\u8bc1\u660e\u8fc7\u7a0b\uff1a\u8bbeA,B\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5373\u6709\u5219

\u81f3\u6b64\uff0c\u6839\u636e\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u5b9a\u4e49\u53ef\u5f97\uff0cA\u00b1B\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002

\u6027\u8d282
\u8bbeA\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5219 \u4ecd\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002
\u8bc1\u660e\u8fc7\u7a0b\uff1a
\u8bbeA\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0c\u5373\u6709\u5219\u6709


\u81f3\u6b64\uff0c\u6839\u636e\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u5b9a\u4e49\u53ef\u5f97\uff0c \u4ecd\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\u3002

\u6027\u8d283
\u8bbeA\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0cB\u4e3a\u5bf9\u79f0\u77e9\u9635\uff0c\u5219AB-BA\u4e3a\u5bf9\u79f0\u77e9\u9635\u3002
\u8bc1\u660e\u8fc7\u7a0b\uff1a
\u5df2\u77e5A\u4e3a\u53cd\u5bf9\u79f0\u77e9\u9635\uff0cB\u4e3a\u5bf9\u79f0\u77e9\u9635\uff0c\u5373\u6709
\u6545\u6709\uff1a
\u81f3\u6b64\uff0c\u6839\u636e\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u5b9a\u4e49\u53ef\u5f97\uff0cAB-BA\u4e3a\u5bf9\u79f0\u77e9\u9635\u3002
\u53c2\u8003\u8d44\u6599:\u767e\u5ea6\u767e\u79d1--\u53cd\u5bf9\u79f0\u77e9\u9635

对称矩阵定义是 A=A的转置
反对称矩阵定义是 A= - A的转置

转置你知道吧? 一个矩阵行列互换就变成它的转置矩阵

或者说 ,反对称矩阵是这样一个矩阵
它的第I行和第I列 各数 绝对值相等,符号相反

反对称矩阵定义是:a=
-
a’(a的转置前加负号)
它的第ⅰ行和第ⅰ列各数绝对值相等,符号相反。即
a(i,j)=-a(i,j)。

看书查啊,大一课本里就有

  • 鑰冪爺鏁板洓
    绛旓細鐭╅樀鐨勬蹇靛崟浣嶇煩闃点佸瑙掔煩闃点佹暟閲忕煩闃点佷笁瑙掔煩闃靛拰瀵圭О鐭╅樀銆佺煩闃电殑鍜屾暟涓庣煩闃电殑绉 鐭╅樀涓庣煩闃电殑绉 鐭╅樀鐨勮浆缃侀嗙煩闃电殑姒傚康鍜屾ц川銆佺煩闃电殑浼撮殢鐭╅樀銆佺煩闃电殑鍒濈瓑鍙樻崲銆佸垵绛夌煩闃点佸垎鍧楃煩闃靛強鍏惰繍绠楃煩闃电殑绉 鑰冭瘯瑕佹眰 1.鐞嗚В鐭╅樀鐨勬蹇,浜嗚В鍑犵鐗规畩鐭╅樀鐨勫畾涔夊拰鎬ц川銆 2.鎺屾彙鐭╅樀鐨勫姞娉曘佹暟涔樺拰涔樻硶浠ュ強瀹冧滑...
  • 濡備綍鐞嗚В鐭╅樀鍚堝悓鐨勫厖瑕佹潯浠?
    绛旓細浜屾鍨嬬敤鐨勭煩闃垫槸瀹瀵圭О鐭╅樀銆備袱涓疄瀵圭О鐭╅樀鍚堝悓鐨勫厖瑕佹潯浠舵槸瀹冧滑鐨勬璐熸儻鎬ф寚鏁扮浉鍚屻傜敱杩欎釜鏉′欢鍙互鎺ㄧ煡锛屽悎鍚岀煩闃电瓑绉┿傜浉浼肩煩闃典笌鍚堝悓鐭╅樀鐨勭З閮界浉鍚屻傝M鏄痭闃跺疄绯绘暟瀵圭О鐭╅樀锛 濡傛灉瀵逛换浣曚竴闈為浂瀹炲悜閲廥锛岄兘浣夸簩娆″瀷f(X)= X鈥睲X>0锛屽垯绉癴(X)涓烘瀹氫簩娆″瀷锛宖(X)鐨勭煩闃礛绉颁负姝e畾鐭╅樀銆
  • 鍏充簬鏁版嵁缁撴瀯鐨勯棶棰,鐢–璇█鎻忚堪
    绛旓細杩欎簺鐭╅樀鍖呮嫭:瀵圭О鐭╅樀,涓夎鐭╅樀,鍏锋湁鏌愮鐗圭偣鐨勭█鐤忕煩闃电瓑銆傜啛鎮夌█鐤忕煩闃电殑涓夌涓嶅悓瀛樺偍鏂瑰紡:涓夊厓缁,甯﹁緟鍔╄鍚戦噺鐨勪簩鍏冪粍,鍗佸瓧閾捐〃瀛樺偍銆傛帉鎻″皢绋鐤忕煩闃电殑涓夊厓缁勬垨浜屽厓缁勫悜鍗佸瓧閾捐〃杩涜杞崲鐨勭畻娉曘4.骞夸箟琛ㄧ殑姒傚康,鐗瑰埆搴旇鏄庣‘琛ㄥご涓庤〃灏剧殑瀹氫箟銆傝繖涓鐐,鏄悊瑙f暣涓箍涔夎〃涓鑺傜畻娉曠殑鍩虹銆傝繎鏉,鍦ㄤ竴浜涘鏍′腑,鍑虹幇浜...
  • 绾挎т唬鏁板彂灞曞彶璇︾粏璧勬枡澶у叏
    绛旓細鍥炵瓟閲:433 閲囩撼鐜:100% 甯姪鐨勪汉:50涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鍏充簬绾挎у彂灞曠殑鍘嗗彶,璁$畻鍗曞厓涓哄悜閲(缁),鐭╅樀,琛屽垪寮忋 鍩烘湰浠嬬粛 涓枃鍚 :绾挎т唬鏁板彂灞曞彶 棰嗗煙:鏁板 璁$畻鍗曞厓 :鍚戦噺(缁),鐭╅樀,琛屽垪寮 姒傚康:鎵鐮旂┒鐨勫叧鑱旀ф槸绾挎 鍩烘湰绠浠,琛屽垪寮,鐭╅樀,鏂圭▼缁,浜屾鍨,浠庤В鏂圭▼鍒扮兢璁,...
  • 瀵圭О鐭╅樀鍖栦负瀵硅闃,璇︾粏鐐瑰摝,璋㈣阿...
    绛旓細涓嶅崟浣嶅寲寰椾笉鍒版浜ょ煩闃 杩介棶 閭e氨鏄瑕佹眰姝d氦鐭╅樀灏卞繀椤诲皢鐗瑰緛鍚戦噺缁欏崟浣嶅寲鍚...?? 鏇村杩介棶 鏈鍥炵瓟鐢辨彁闂呮帹鑽 涓炬姤| 璇勮 8 1 lry31383 閲囩撼鐜:88% 鏉ヨ嚜鍥㈤槦:鏁板杈呭鍥 鎿呴暱: 鏁板 瀛︿範甯姪 鐞嗗伐瀛︾ 鏁欒偛/绉戝 鑰冪爺 涓烘偍鎺ㄨ崘: 瀹炲绉扮煩闃 浠涔堟槸瀵圭О鐭╅樀 姝e畾鐭╅樀 鐭╅樀涔樻硶 瀵圭О鐭╅樀瀵硅...
  • 鏁版嵁缁撴瀯瀵圭О鐭╅樀鐨勫帇缂╁瓨鍌ㄦ眰鏁版嵁鍦板潃
    绛旓細鍏朵粬鍥炵瓟 棣栧厛瑕佸厛鐪嬬湅鐭╅樀鐨勮鍒楄〃,鏈夋椂浼氫粠1寮濮,浣嗛粯璁ゆ槸浠0寮濮嬪緢鏄剧劧,杩欓噷缁欏嚭鐨勬槸a[0][0]琛屽垪琛ㄥ氨鏄粠0寮濮嬬殑鎵浠[3][6]灏辨槸绗3琛岀殑绗6涓厓绱(杩欓噷鐨3鍜6鎸囩殑鏄笅鏍,瀹為檯涓婃槸绗4琛岀6涓厓绱)鍥犱负a[3][6]鏄笂涓夎鐨勫厓绱,鎵浠ヨ浆鎹㈡垚涓嬩笁瑙掑氨鏄痑[6][3]鍥犱负瀵圭О鐭╅樀鍙渶瀛樺偍涓嬩笁瑙掓垨涓...
  • 鈥滄浜鐭╅樀涓瀹氭槸姝e畾鐭╅樀鈥濋敊,姹傜悊鐢,鍙嶄緥涔熻,璇︾粏,璋㈣阿
    绛旓細浣犲ソ锛侀敊銆鐭╅樀姝e畾鐨勫墠鎻鏄绉闃碉紝鑰屾浜ょ煩闃典笉涓瀹氭槸瀵圭О闃点傜粡娴庢暟瀛﹀洟闃熷府浣犺В绛旓紝璇峰強鏃堕噰绾炽傝阿璋紒
  • 鐭╅樀鐨勯潪闆跺瓙寮忔槸浠涔鎰忔?
    绛旓細鍏朵粬鍥炵瓟 闈為浂瀛愬紡灏辨槸涓嶄负0鐨勫瓙寮忋 鐑績缃戝弸| 鍙戝竷浜2012-12-07 涓炬姤| 璇勮 0 16 1鏉℃姌鍙犲洖绛 涓烘偍鎺ㄨ崘: 鐭╅樀鐨勭З 浼撮殢鐭╅樀 姝e畾鐭╅樀 閫嗙煩闃 鐭╅樀涔樻硶 鐭╅樀鐩镐技 瀵圭О鐭╅樀 鍗曚綅鐭╅樀 姝d氦鐭╅樀 鐭╅樀鐨勭З涓庢柟绋嬬粍鐨勮В 鍏朵粬绫讳技闂...
  • 璇烽棶璋佺煡閬撻珮鏁颁笂涓嬪摢浜涚珷鑺(鍏蜂綋鍒板摢浜涘皬鑺)鏄冪爺鏁颁笁涓嶈冪殑?
    绛旓細妤间笂鐨勬病鐪嬫竻妤氶棶棰樺摝 妤间富鍙棶浜嗛珮鏁伴儴鍒嗭紝鎴戠殑鍥炵瓟濡備笅锛2009骞磋冪爺鏁板澶х翰鍐呭 鏁颁笁 寰Н鍒 涓銆佸嚱鏁般佹瀬闄愩佽繛缁 鑰冭瘯鍐呭 鍑芥暟鐨勬蹇靛強琛ㄧず娉 鍑芥暟鐨勬湁鐣屾э紟鍗曡皟鎬э紟鍛ㄦ湡鎬у拰濂囧伓鎬 澶嶅悎鍑芥暟锛庡弽鍑芥暟锛庡垎娈靛嚱鏁板拰闅愬嚱鏁 鍩烘湰鍒濈瓑鍑芥暟鐨勬ц川鍙婂叾鍥惧舰 鍒濈瓑鍑芥暟 鍑芥暟鍏崇郴鐨勫缓绔 鏁板垪鏋侀檺涓庡嚱鏁版瀬闄...
  • 鏃犺鏈夊悜鍥捐繕鏄棤鍚戝浘,椤剁偣鏁皀,杈规暟e鍜屽害鏁颁箣闂存湁浠涔鍏崇郴
    绛旓細鎬诲害鏁(D)绛変簬杈规暟(e)鐨勪袱鍊嶃侱=2e 鍥綠鐨勯《鐐规暟n鍜岃竟鏁癳鐨勫叧绯 1銆佽嫢G鏄棤鍚戝浘锛屽垯0鈮鈮(n-1)/2銆傛伆鏈塶(n-1)/2鏉¤竟鐨勬棤鍚戝浘绉版棤鍚戝畬鍏ㄥ浘(Undireet-ed Complete Graph)銆2銆佽嫢G鏄湁鍚戝浘锛屽垯0鈮鈮(n-1)銆傛伆鏈塶(n-1)鏉¤竟鐨勬湁鍚戝浘绉颁负鏈夊悜瀹屽叏鍥(Directed Complete ...
  • 扩展阅读:扫一扫题目出答案 ... 杨建平禁赛原因的详细回答 ... 对称图形图片大全 ... 详细回答工具书的种类 ... 详细回答工具书的功能 ... 反对称行列式计算方法 ... 反对称矩阵图 ... 对称点万能公式 ... 什么是反对称矩阵 举例 ...

    本站交流只代表网友个人观点,与本站立场无关
    欢迎反馈与建议,请联系电邮
    2024© 车视网