矩阵的初等变换时可以提取个负号吗 矩阵能不能单独从一行提出一个负号?
\u521d\u7b49\u77e9\u9635\u884c\u521d\u7b49\u53d8\u6362A\u4ea4\u6362\u4e24\u884c\u662f\u5426\u53ef\u4ee5\u5728\u53f3\u8fb9\u6dfb\u52a0\u8d1f\u53f7\uff08\u9644\u56fe\uff09\uff08A,E)\u5176\u5b9e\u662f\u5206\u5757\u77e9\u9635\uff0c\u5bf9A\u505a\u521d\u7b49\u884c\u53d8\u6362\uff0c\u76f8\u5f53\u4e8e\u7528\u5bf9\u5e94\u521d\u7b49\u77e9\u9635\u5de6\u4e58A\u3002\u521d\u7b49\u884c\u53d8\u6362\u53ea\u6709\u4ea4\u6362\u4e24\u884c\u3001\u500d\u4e58\u3001\u500d\u52a03\u79cd\uff0c\u6240\u4ee5\u5bf9\u5e94\u521d\u7b49\u77e9\u9635\u4e5f\u6709Eij,EI(k),Eij(k)\u4e09\u79cd\u3002\u4ea4\u6362\u4e24\u884c\u4e0d\u7528\u5728\u53f3\u8fb9\u52a0\u8d1f\u53f7\u3002\u521d\u7b49\u884c\u53d8\u6362\u65bd\u52a0\u7684\u5bf9\u8c61\u662fA\u548cE\u7684\u6574\u4f53\u3002\u82e5\u5728\u53f3\u8fb9\u67d0\u884c\u6dfb\u52a0\u8d1f\u53f7\uff0c\u5373\u7528-1\u4e58\u4ee5\u67d0\u884c\uff0c\u5219\u5de6\u8fb9\u77e9\u9635\u4e5f\u8981\u4e58\u4ee5-1\uff0c\u5373\u53d8\u53f7\u3002
\u77e9\u9635\u4e0d\u80fd\u5355\u72ec\u4ece\u4e00\u884c\u63d0\u51fa\u4e00\u4e2a\u8d1f\u53f7\u3002\u56e0\u4e3a\u5982\u679c\u60f3\u8981\u4ece\u77e9\u9635\u4e2d\u63d0\u51fa\u4e00\u4e2a\u8d1f\u53f7\uff0c\u77e9\u9635\u5168\u90e8\u5143\u7d20\u9700\u8981\u4e00\u8d77\u63d0\u5230\u524d\u9762\uff0c\u8fd9\u91cc\u533a\u522b\u4e0e\u884c\u5217\u5f0f\uff0c\u884c\u5217\u5f0f\u53ef\u4ee5\u5355\u72ec\u4ece\u4e00\u884c\u4e2d\u63d0\u51fa\u516c\u56e0\u6570\u3002
1\u3001\u77e9\u9635\u7684\u6570\u4e58\u6ee1\u8db3\u4ee5\u4e0b\u8fd0\u7b97\u5f8b\uff1a
2\u3001\u77e9\u9635\u7684\u52a0\u6cd5\u6ee1\u8db3\u4e0b\u5217\u8fd0\u7b97\u5f8b(A\uff0cB\uff0cC\u90fd\u662f\u540c\u578b\u77e9\u9635)\uff1a
\u53ea\u6709\u540c\u578b\u77e9\u9635\u4e4b\u95f4\u624d\u53ef\u4ee5\u8fdb\u884c\u52a0\u6cd5\uff0c\u77e9\u9635\u7684\u52a0\u51cf\u6cd5\u548c\u77e9\u9635\u7684\u6570\u4e58\u5408\u79f0\u77e9\u9635\u7684\u7ebf\u6027\u8fd0\u7b97\u3002
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u77e9\u9635\u7684\u4e58\u6cd5
\uff081\uff09\u7ed3\u5408\u5f8b\uff1a
\uff082\uff09\u5de6\u5206\u914d\u5f8b\uff1a
\uff083\uff09\u53f3\u5206\u914d\u5f8b\uff1a
2\u3001\u77e9\u9635\u7684\u8ff9\uff1a
\u77e9\u9635A\u7684\u5bf9\u89d2\u5143\u7d20\u4e4b\u548c\u79f0\u4e3a\u77e9\u9635A\u7684\u8ff9(trace),\u8bb0\u4f5ctr\uff08A\uff09\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u77e9\u9635
但如果是为了求行列式，要注意是否改变行列式的值
可以啊，就是在数乘c
绛旓細閫嗙煩闃靛張鏄煩闃电悊璁虹殑寰堥噸瑕佺殑鍐呭锛岄鐭╅樀鐨姹傛硶鑷劧涔熷氨鎴愪负绾挎т唬鏁扮爺绌剁殑涓昏鍐呭涔嬩竴銆傝A鏄暟鍩熶笂鐨勪竴涓猲闃舵柟闃碉紝鑻ュ湪鐩稿悓鏁板煙涓婂瓨鍦ㄥ彟涓涓猲闃剁煩B锛屼娇寰楋細AB=BA=E銆 鍒欐垜浠ОB鏄疉鐨勯嗙煩闃碉紝鑰孉鍒欒绉颁负鍙嗙煩闃点傚叾涓紝E涓哄崟浣嶇煩闃点傚吀鍨嬬殑鐭╅樀姹傞嗘柟娉曟湁锛氬埄鐢ㄥ畾涔夋眰閫嗙煩闃点鍒濈瓑鍙樻崲娉...
绛旓細x3=0,x5=0,鐪嬫渶鍚庝竴鍒椾笌閭ｄ笁涓1瀵瑰簲鐨勬暟 x1=-8,x2=3,x4=2 ,鍗冲緱鐗硅В (-8,3,0,2,0)^T 姹侫X=0鐨勫熀纭瑙ｇ郴鏃,浠3=1,x5=0 鐪嬬3鍒椾笌閭ｄ笁涓1瀵瑰簲鐨勬暟(鍙鐩稿弽鏁),寰 (0,-2,1,0,0)^T 浠3=0,x5=1 鐪嬬5鍒椾笌閭ｄ笁涓1瀵瑰簲鐨勬暟(鍙栫浉鍙嶆暟),寰 (-4,3,0,-2,1)^T...
绛旓細鍙互鎻愬嚭闈為浂鍏洜瀛 浣嗘彁鍑哄悗灏辨墧浜 杩欎釜闈為浂鍏洜瀛愭病鐢 杩欑浉褰撲簬鏌愯涔樹竴涓潪闆剁殑鏁 (绗2涓鍒濈瓑琛鍙樻崲)
绛旓細鐗规畩鐨勶紝渚嬪涓涓煩闃碉紝姣忚姣忓垪閮戒负1锛屽叾鐗瑰緛鍊间负0锛岀粡杩鍒濈瓑鍙樻崲鍚庯紝鍏剁壒寰佸间粛涓0銆鐭╅樀鍙樻崲鏄嚎鎬т唬鏁颁腑鐭╅樀鐨涓绉嶈繍绠楀舰寮忋傛湁浠ヤ笅涓夌鍙樻崲绫诲瀷锛1銆佷氦鎹㈢煩闃电殑涓よ銆2銆佷互涓涓潪闆舵暟k涔樼煩闃电殑鏌愪竴琛屾墍鏈夊厓绱犮3銆佹妸鐭╅樀鐨勬煇涓琛屾墍鏈夊厓绱犱箻浠ヤ竴涓暟k鍚庡姞鍒板彟涓琛屽搴旂殑鍏冪礌銆
绛旓細鍒濈瓑鍙樻崲鏄妸涓涓煩闃靛彉鍖栧彟涓涓煩闃碉紝涓棿鏄敤绠ご杩炴帴锛屼笉瀛樺湪鐩哥瓑鍏崇郴锛屾墍浠ヨ嫢鏌愯鎻愬嚭涓涓叕鍥犲瓙锛岀洿鎺ユ妸瀹冨幓鎺夊氨鍙互浜嗐傚鏋滄嫭鍙峰鍐欎竴涓嶆暟锛屾槸瀵规暣涓鐭╅樀鐨鎵鏈夊厓绱犱箻鍊嶆暟锛岃繖鏍峰弽鑰屽嚭閿欎簡銆
绛旓細瑕佹浛鎹㈠氨瑕佹壘鐩稿簲鐨勪緷鎹紝涓嶈璇曞浘鍘昏儗缁撹锛屾垨鑰呮悶浠涔堝綊绾虫荤粨锛岄亣鍒板叿浣撴儏鍐垫妸鐩稿簲鐨勪緷鎹悶娓呮灏辫浜 姣斿璇翠綘鍋鐨勫垵绛夊彉鎹鐩稿綋浜嶢=LB锛岄偅涔圓^{-1}=B^{-1}L^{-1}锛宒et(A)=det(L)det(B)锛屸︹︽湁鏃跺洜涓烘湁det(L)=1鎵嶄細璁╀綘瑙夊緱det(A)=det(B)濂藉儚鏄竴涓洿鎺ョ殑鏇挎崲锛屼絾鎼炴竻妤氬師鐞嗗氨...
绛旓細鐢ㄧ涓夌被鍒濈瓑鍙樻崲鍙互瀹炵幇(x,y) -> (-y,x)鐨勫彉鎹, 鍏蜂綋濡備笅 (x,y) -> (x,x+y) -> (-y,x+y) -> (-y,x)2) 鏃㈢劧鏈変簡琛屼氦鎹(宸竴涓礋鍙)鍜岀涓夌被鍒濈瓑鍙樻崲, 閭ｄ箞灏卞彲浠ヤ娇鐢℅auss娑堝幓娉, 鎶夾鍖栨垚瀵硅闃.3) 褰搙y鈮0鏃剁涓夌被鍒濈瓑鍙樻崲鍙互鎶奷iag{x,y}鍙樺埌diag{1,xy}, 鍏蜂綋濡...
绛旓細鎴戜篃鍋氫笉濂斤紝琛屽垪寮鍙樻崲锛岄伒寰6涓ц川鑰屾潵锛鐭╅樀閬靛惊3涓彉鎹㈡ц川鑰屽畾锛屽尯鍒氨鏄繖浜涗簡锛屾庝箞鎵嶈兘鍙樻垚闇瑕佺殑褰㈠紡锛屽氨瑕佽嚜宸卞仛棰樹簡锛屾病鍒殑鏂规硶锛屼竴涓畝鍗曠殑鐭╅樀锛屾垜鍋氫簡6娆★紝鍙樹簡涓嶅悓鐨勬柟娉曪紝鏈鍚庣粓浜3绉嶆柟娉曟槸姝ｇ‘鐨勶紝鍙兘杩欐牱浜嗐
绛旓細=5x+5锛鍒濈瓑鍙樻崲灏卞ソ鍍忔槸鎴戣鎶妜+1鍙樻垚5x+1锛岃岃繖涓敼鍙樺湪鍙︿竴浜涘湴鏂癸紙姣斿瑙ｆ柟绋嬶級涓婇潰寰堟湁鐢 鍙兘浣犺繕娌℃帴瑙﹀埌鍚庨潰涓句釜绠鍗曠殑渚嬪瓙锛屽氨鍍忎綘瑙ｄ簩鍏冧竴娆℃柟绋嬫椂鍊欎竴鏍凤紝鍏朵腑涓涓柟绋嬩箻浠ヤ竴涓父鏁扮劧鍚庝袱涓柟绋嬬浉鍑忔秷鍘绘湭鐭ユ暟锛屽垵绛夊彉鎹㈠氨鏄繖涓繃绋嬶紝鍙笉杩鐭╅樀灏卞ソ鍍忎竴涓緢澶氭湭鐭ユ暟鐨勬柟绋嬩竴鏍 ...
绛旓細鎴戜滑涔熸槸杩欎箞鍋氱殑锛岀啛鑳界敓宸 璇烽棶鍦鍒濈瓑鍙樻崲鐨勬椂鍊锛屾庢牱瑙傚療鎬庢牱鍖栨瘮杈冨ソ锛熷湪鐭╅樀杩涜鍒濈瓑鍙樻崲鐨勬椂鍊欙紝鍙互鍚屾椂杩涜琛屾垨鍒楃殑杞崲鍚楋紵涓嶅彲浠ヨ繘琛岀殑锛屼竴鏃︿綘鍐欐垚锛圓|E锛=銆嬶紙鍐欐垚锛圓 寰 (E |E锛 |B锛夋潵鍙樻崲鏃跺彧鑳界敤鍒楀彉鎹備綘濡傛灉瑙夊緱绻佺悙鍙互鎵惧嚑涓疄渚嬫潵鍖栫畝涓涓嬨
