矩阵的伴随矩阵、逆矩阵、转置矩阵之间的关系 有人能跟我解释下什么是“逆矩阵 转置矩阵 数量阵 伴随矩阵”...
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2 0 0
0 1 0
0 0 3
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=
1/2 0 0
0 1 0
0 0 1/3
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=
k 0 0
0 k 0
0 0 k
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A*=
3 0 0
0 6 0
0 0 2
A逆 = A*/|A|
(A逆)转置 = (A转置)逆
绛旓細0 0 3 閫嗙煩闃礎^(-1)锛屽氨鏄弧瓒矨B=BA=E鐨勭煩闃礏 = 1/2 0 0 0 1 0 0 0 1/3 杞疆鐭╅樀A^T,灏辨槸灏咥鐨勮涓庡垪浜掓崲 鏈緥瀛愶紝鍥犱负A鏄绉伴樀锛岃浆缃氨绛変簬鑷韩锛屽嵆A^T=A 鏁伴噺闃碉紝灏辨槸鍗曚綅鐭╅樀鎴愬嶆暟鍏崇郴鐨勭煩闃碉紝鍗砶E = k 0 0 0 k 0 0 0 k 浼撮殢鐭╅樀锛屽氨鏄疉 鍗矨鐨勬瘡涓厓绱狅紝鏇...
绛旓細涓夎呬腑浠绘剰涓ょ杩愮畻缁撳悎锛屼笌娆″簭鏃犲叧銆備緥濡傜煩闃礎鐨杞疆鐭╅樀鐨勯嗙煩闃绛変簬A鐨閫嗙煩闃电殑杞疆鐭╅樀銆
绛旓細a鐨勪即闅忕煩闃垫庝箞姹濡備笅锛氱洿鎺ヨ绠楁硶:璁＄畻鐭╅樀A鐨勪即闅忕煩闃礎,鍙互鐩存帴璁＄畻A*=det(A)A^(-1),鍏朵腑det(A)琛ㄧず鐭╅樀A鐨勮鍒楀紡,A^(-1)琛ㄧず鐭╅樀A鐨閫嗙煩闃銆傞嗙煩闃佃绠楁硶:璁＄畻鐭╅樀A鐨勪即闅忕煩闃礎,鍙互鍏堣绠楃煩闃礎鐨勯嗙煩闃礎^(-1),鐒跺悗鍐嶈绠桝*=A^(-1)T,鍏朵腑T琛ㄧず鐭╅樀A鐨杞疆鐭闃点備即闅忕煩闃电畝浠嬶細鍦...
绛旓細涓銆佸惈涔変笉鍚岋細1銆佸湪绾挎т唬鏁颁腑锛屼竴涓柟褰鐭╅樀鐨勪即闅忕煩闃鏄竴涓被浼间簬閫嗙煩闃鐨勬蹇点傚鏋滀簩缁鐭╅樀鍙嗭紝閭ｄ箞瀹冪殑閫嗙煩闃靛拰瀹冪殑浼撮殢鐭╅樀涔嬮棿鍙樊涓涓郴鏁帮紝瀵瑰缁寸煩闃典篃瀛樺湪杩欎釜瑙勫緥銆傜劧鑰岋紝浼撮殢鐭╅樀瀵逛笉鍙閫嗙殑鐭╅樀涔熸湁瀹氫箟锛屽苟涓斾笉闇瑕佺敤鍒伴櫎娉曘2銆佸皢鐭╅樀鐨勮鍒椾簰鎹㈠緱鍒扮殑鏂扮煩闃电О涓杞疆鐭╅樀锛杞疆鐭╅樀鐨...
绛旓細涓銆佸惈涔変笉鍚岋細1銆佽浆缃煩闃碉細灏嗙煩闃电殑琛屽垪浜掓崲寰楀埌鐨勬柊鐭╅樀绉颁负杞疆鐭╅樀锛杞疆鐭╅樀鐨勮鍒楀紡涓嶅彉銆2銆佷即闅忕煩闃碉細鍦ㄧ嚎鎬т唬鏁颁腑锛屼竴涓柟褰鐭╅樀鐨勪即闅忕煩闃鏄竴涓被浼间簬閫嗙煩闃鐨勬蹇点傚鏋滀簩缁鐭╅樀鍙嗭紝閭ｄ箞瀹冪殑閫嗙煩闃靛拰瀹冪殑浼撮殢鐭╅樀涔嬮棿鍙樊涓涓郴鏁帮紝瀵瑰缁寸煩闃典篃瀛樺湪杩欎釜瑙勫緥銆傜劧鑰岋紝浼撮殢鐭╅樀瀵逛笉鍙嗙殑...
绛旓細涓銆佹暟瀛﹀師鐞嗕笉鍚 鍦ㄧ嚎鎬т唬鏁颁腑锛屼竴涓柟褰鐭╅樀鐨勪即闅忕煩闃鏄竴涓被浼间簬閫嗙煩闃鐨勬蹇 [1] 銆傚鏋滀簩缁鐭╅樀鍙嗭紝閭ｄ箞瀹冪殑閫嗙煩闃靛拰瀹冪殑浼撮殢鐭╅樀涔嬮棿鍙樊涓涓郴鏁帮紝瀵瑰缁寸煩闃典笉瀛樺湪杩欎釜瑙勫緥銆傜劧鑰岋紝浼撮殢鐭╅樀瀵逛笉鍙閫嗙殑鐭╅樀涔熸湁瀹氫箟锛屽苟涓斾笉闇瑕佺敤鍒伴櫎娉 銆傝A鏄暟鍩熶笂鐨勪竴涓猲闃鐭╅樀锛鑻ュ湪鐩稿悓鏁板煙涓婂瓨...
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绛旓細銆愬尯鍒杞疆鐭闃靛彧灏嗗師鐭╅樀琛屽彉鍒楋紙鍒楀彉琛岋級娌℃湁浣滀换浣曡繍绠椼備即闅忕煩闃垫槸鍏堣姹傚師鐭╅樀鐨勪唬鏁颁綑瀛愬紡锛屽苟鎸夎浆缃柟寮忔斁鍦ㄧ浉搴旂殑浣嶇疆涓婏紙濡俛12鐨勪唬鏁颁綑瀛愬紡鏀惧湪绗簩琛屻佺涓鍒楃殑浣嶇疆涓娿傘愰檮銆戜即闅忕煩闃电殑浠嬬粛 鍦ㄧ嚎鎬т唬鏁颁腑锛屼竴涓柟褰鐭╅樀鐨勪即闅忕煩闃鏄竴涓被浼间簬閫嗙煩闃鐨勬蹇点傚鏋鐭╅樀鍙嗭紝閭ｄ箞瀹冪殑閫...
绛旓細浜岄樁鐭╅樀姹備即闅忓彛璇锛氫富瀵硅皟锛屽壇鍙樺彿銆傦紙鍗充富瀵硅绾夸笂鍏冪礌璋冩崲浣嶇疆锛屽壇瀵硅绾夸笂鍏冪礌鏀瑰彉姝ｈ礋鍙凤級鍘熺悊鏄眰鍑哄悇鍏冪礌鐨勪唬鏁颁綑瀛愬紡锛屽啓鍦ㄥ搴斾綅缃紝鐒跺悗杞疆銆傚湪绾挎т唬鏁颁腑锛屼竴涓柟褰鐭╅樀鐨勪即闅忕煩闃鏄竴涓被浼间簬閫嗙煩闃鐨勬蹇点傚鏋滀簩缁鐭╅樀鍙嗭紝閭ｄ箞瀹冪殑閫嗙煩闃靛拰瀹冪殑浼撮殢鐭╅樀涔嬮棿鍙樊涓涓郴鏁帮紝瀵瑰缁寸煩闃...
绛旓細1銆佷即闅忕煩闃垫硶 濡傛灉鐭╅樀A鍙嗭紝鍒 鐨勪綑鍥犲瓙鐭╅樀鐨勮浆缃煩闃銆傦紙|A|鈮0锛寍A|涓鸿鐭╅樀瀵瑰簲鐨勮鍒楀紡鐨勫硷級A鐨勪即闅忕煩闃涓 鍏朵腑Aij=锛-1锛塱+jMij绉颁负aij鐨勪唬鏁颁綑瀛愬紡銆2銆佸垵绛夎鍙樻崲娉 鍦ㄨ闃舵鐭╅樀鐨勫熀纭涓婏紝鍗抽潪闆惰鐨勭涓涓潪闆跺崟鍏冧负1锛屼笖杩欎簺闈為浂鍗曞厓鎵鍦ㄧ殑鍒楀叾瀹冨厓绱犻兘鏄0銆傜患涓婏紝琛屾渶绠...
