共轭转置的定义 共轭转置的性质
\u4ec0\u4e48\u662f\u5171\u8f6d\u8f6c\u7f6e\u77e9\u9635\u5177\u4f53\u610f\u601d\u5982\u4e0b\uff1a
\u5171\u8f6d\u5c31\u662f\u77e9\u9635\u6bcf\u4e2a\u5143\u7d20\u90fd\u53d6\u5171\u8f6d\uff08\u5b9e\u90e8\u4e0d\u53d8\uff0c\u865a\u90e8\u53d6\u8d1f\uff09\u3002
\u8f6c\u7f6e\u5c31\u662f\u628a\u77e9\u9635\u7684\u6bcf\u4e2a\u5143\u7d20\u6309\u5de6\u4e0a\u5230\u53f3\u4e0b\u7684\u6240\u6709\u5143\u7d20\u5bf9\u79f0\u8c03\u6362\u8fc7\u6765\u3002
\u5171\u8f6d\u8f6c\u7f6e\u5c31\u662f\u5148\u53d6\u5171\u8f6d\uff0c\u518d\u53d6\u8f6c\u7f6e\u3002
\u4ee5\u590d\u6570\u4e3a\u5143\u7d20\u7684\u77e9\u9635\uff0c\u5176\u5171\u8f6d\u77e9\u9635\u6307\u5bf9\u6bcf\u4e00\u4e2a\u5143\u7d20\u53d6\u5171\u8f6d\u4e4b\u540e\u5f97\u5230\u7684\u77e9\u9635\u3002
\u5171\u8f6d\u77e9\u9635\u53c8\u79f0Hermite\u9635\uff0c\u6bcf\u4e00\u4e2a\u7b2ci\u884c\u7b2cj\u5217\u7684\u5143\u7d20\u90fd\u4e0e\u7b2cj\u884c\u7b2ci\u5217\u7684\u5143\u7d20\u7684\u5171\u8f6d\u76f8\u7b49\u3002
\u62d3\u5c55\u8d44\u6599\uff1a
\u82e5\u77e9\u9635A\u3001B\u7ef4\u6570\u76f8\u540c\uff0c\u5219(A + B)* = A* + B*\u3002
(rA)* = r*A*\uff0c\u5176\u4e2dr\u4e3a\u590d\u6570\uff0cr*\u4e3ar\u7684\u590d\u5171\u8f6d\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u5171\u8f6d\u8f6c\u7f6e
(AB)* = B*A*\uff0c\u5176\u4e2dA\u4e3am\u884cn\u5217\u7684\u77e9\u9635\uff0cB\u4e3an\u884cp\u5217\u77e9\u9635\u3002(A*)* = A\u82e5A\u4e3a\u65b9\u9635\uff0c\u5219det(A*) = (det A)*\uff0c\u4e14tr(A*) = (tr A)*A\u662f\u53ef\u9006\u77e9\u9635\uff0c \u5f53\u4e14\u4ec5\u5f53 A*\u53ef\u9006\uff0c\u4e14\u6709inv(A*) = (inv(A))*\u4e0a\u5f0finv\u8868\u793a\u77e9\u9635\u7684\u9006\u3002.A*\u7684\u7279\u5f81\u503c\u662fA\u7684\u7279\u5f81\u503c\u7684\u590d\u5171\u8f6d\u3002 = \uff0c\u5176\u4e2dA\u4e3am\u884cn\u5217\u7684\u77e9\u9635\uff0c\u590d\u5411\u91cfx\u4e3an\u7ef4\u5217\u5411\u91cf\uff0c\u590d\u5411\u91cfy\u4e3am\u7ef4\u5217\u5411\u91cf\uff0c\u4e3a\u590d\u6570\u7684\u5185\u79ef\u3002
矩阵 A 的共轭转置A * 定义为:
其中表示矩阵i行j列上的元素，表示标量的复共轭。
这一定义也可以写作：
其中是矩阵A的转置， 表示对矩阵A中的元素取复共轭！
绛旓細鐗瑰緛鍊肩浉鍚岋紝涓嶄竴瀹氱浉浼硷紝涔熶笉涓瀹氬悎鍚屻備絾鏄:1锛夊鏋滈兘鏄绉扮煩闃碉紝閭ｄ箞鐗瑰緛鍊肩浉鍚岋紝鑳芥帹鍑哄悎鍚 2锛夊鏋滀袱鐭╅樀閮藉彲浠ョ浉浼煎瑙掑寲锛屽垯涓ょ煩闃电壒寰佸肩浉鍚岋紝鑳芥帹鍑虹浉浼笺
绛旓細ans= 2 8 1 9 10 9 4 5 1 9 3 1 浜屻侀浂鐭╅樀 zeros(5):鐢熸垚浜旇浜斿垪鐨勯浂鐭╅樀 zeros(5) ans= 0 0 0 0 0 ...鐮佸啘缃2022-04-06 鐩稿叧鎼滅储 杞疆鍏辫江 鍏辫江杞疆 浠涔堟槸鍏辫江杞疆 鍏辫江杞疆鍜岃浆缃殑鍖哄埆 鐭╅樀涔樼煩闃电殑鍏辫江杞疆绛変簬浠涔 鍏辫江杞疆鐨鎬ц川 鐭╅樀涔樼Н鐨勫叡杞浆缃 鐭╅樀鍏辫江杞疆瀹氫箟 ...
绛旓細棣栧厛锛屾垜浠潵瀹氫箟鍏辫江鐭╅樀銆傚浜庝竴涓鏁扮煩闃礎锛屽叾鍏辫江鐭╅樀A*鏄皢姣忎釜鍏冪礌aij鐨勫疄閮ㄤ繚鎸佷笉鍙橈紝鑰岃櫄閮ㄥ彇鐩稿弽鏁板緱鍒扮殑鏂扮煩闃点傚嵆瀵逛簬浠绘剰鐨勫鏁癮+bi锛屽叾鍏辫江涓篴-bi銆傚洜姝わ紝涓涓猲闃跺鏁扮煩闃礎鐨勫叡杞煩闃礎*鏄竴涓猲闃跺鏁扮煩闃碉紝婊¤冻A*=A^T*(A^T琛ㄧずA鐨勮浆缃)銆傛帴涓嬫潵锛屾垜浠潵瀹氫箟杞疆鐭╅樀銆傚浜庝竴涓猲...
绛旓細鍏辫江杞疆鐭╅樀鏄嚎鎬т唬鏁颁腑鐨勪竴涓噸瑕佹蹇碉紝瀹冩槸灏嗕竴涓鏁扮煩闃电殑琛屽拰鍒椾簰鎹紝骞跺皢鎵鏈夊厓绱犲彇鍏跺叡杞鏁板緱鍒扮殑鏂扮煩闃点傛眰鍏辫江杞疆鐭╅樀鐨勬柟娉曞涓嬶細1.棣栧厛锛屾垜浠渶瑕佺煡閬撲竴涓鏁扮煩闃礎鏄竴涓猰脳n鐨勭煩闃碉紝鍏朵腑m琛ㄧず琛屾暟锛宯琛ㄧず鍒楁暟銆2.鐒跺悗锛屾垜浠皢鐭╅樀A鐨勮鍜屽垪浜掓崲锛屽緱鍒颁竴涓柊鐨刴脳n鐭╅樀B銆傝繖涓柊...
绛旓細鍦ㄥ寲瀛︿腑锛鍏辫江閿寚鐨勬槸鍒嗗瓙涓浉閭荤殑涓や釜鍙岄敭涓紝鍏朵腑涓涓弻閿笂鐨勏鐢靛瓙寮ユ暎鍒板彟澶栦竴涓弻閿笂鐨勭幇璞°傝繖绉嶇幇璞′細褰卞搷鍒嗗瓙鐨勭ǔ瀹氭у拰鍙嶅簲鎬ц兘锛屽洜姝ゅ湪鏈夋満鍖栧涓叿鏈夐噸瑕佹剰涔夈傚叡杞殑姒傚康涓杞疆鐨姒傚康涓嶅悓銆傚湪鐭╅樀鍜屽悜閲忎腑锛岃浆缃寚鐨勬槸灏嗙煩闃垫垨鍚戦噺鐨勮鍒椾簰鎹㈢殑鎿嶄綔锛岃屼笉娑夊強瀵瑰厓绱犵殑鎿嶄綔銆"鍏辫江"杩欎釜...
绛旓細涓嶄竴鏍枫鍏辫江杞疆鐨鎬ц川锛(AB)* = B*A*锛屽叾涓瑼涓簃琛宯鍒楃殑鐭╅樀锛孊涓簄琛宲鍒楃煩闃点(A*)* = A 鑻涓烘柟闃碉紝鍒檇et(A*) = (det A)*锛屼笖tr(A*) = (tr A)A鏄彲閫嗙煩闃碉紝 褰撲笖浠呭綋 A*鍙嗭紝涓旀湁inv(A*) = (inv(A))涓婂紡inv琛ㄧず鐭╅樀鐨勯嗐.A*鐨勭壒寰佸兼槸A鐨勭壒寰佸肩殑澶嶅叡杞<...
绛旓細鏍规嵁鍏辫江鐨勫畾涔锛屽鍑芥暟涓殑姣忎釜缁勬垚閮ㄥ垎杩涜鍏辫江鎿嶄綔銆傚浜庡鏁帮紝杩欐剰鍛崇潃灏嗚櫄閮ㄥ彇鍙嶏紱瀵逛簬鍚戦噺鎴栫煩闃碉紝杩欐剰鍛崇潃鎸夌収鍏辫江鐨勮鍒欒繘琛杞疆鎴栧叾浠栨搷浣溿傚鏋滃師鍑芥暟鏄鍚堝嚱鏁帮紝閭ｄ箞闇瑕佸鍐呭涓や釜鍑芥暟鍒嗗埆杩涜鍏辫江鎿嶄綔銆傚鏋滃師鍑芥暟鍖呭惈澶氶」寮忋佹寚鏁般佸鏁扮瓑杩愮畻锛岄偅涔堥渶瑕佸杩欎簺杩愮畻鐨勭粨鏋滆繘琛屽叡杞搷浣溿傛渶缁堝緱鍒扮殑...
绛旓細鐭╅樀鐨鍏辫江杞疆瀹氫箟涓猴細锛屼篃鍙互鍐欎负锛氭垨鑰呭啓涓 銆備竴涓2脳2澶嶆暟鐭╅樀鐨勫叡杞浆缃涓嬫墍绀猴細鎴杗闃舵柟闃 涓や釜鐭╅樀鐨勪箻娉曚粎褰撶涓涓煩闃礎鐨勫垪鏁板拰鍙︿竴涓煩闃礏鐨勮鏁扮浉绛夋椂鎵嶈兘瀹氫箟銆傚A鏄痬脳n鐭╅樀鍜孊鏄痭脳p鐭╅樀锛屽畠浠殑涔樼НC鏄竴涓猰脳p鐭╅樀 锛屽畠鐨勪竴涓厓绱狅細骞跺皢姝や箻绉涓:[9] .渚嬪锛氱煩闃电殑...
绛旓細瀵逛簬澶嶇煩闃佃岃█鍏辫江杞疆纭疄姣斿崟绾殑杞疆鏇翠负甯哥敤, 鍏跺師鍥犱富瑕佹潵鑷簬瀵瑰唴绉殑闇姹 鍏堢湅C^n绌洪棿, x^Ty鏄竴涓弻绾挎у舰寮, 涓嶆瀯鎴愬唴绉, 鑰寈^Hy鎵嶆瀯鎴愬唴绉. 杩涗竴姝, 鐪嬬嚎鎬х畻瀛愮殑浼撮殢, =, 瀹规槗楠岃瘉浼撮殢绠楀瓙鐨勭煩闃佃〃绀烘伆濂芥槸涓涓杞疆鍏辫江. 杩欎簺閮芥槸鐢卞唴绉┖闂寸殑鍏悊鑷劧鍐冲畾鐨. 鎵浠ヤ笌鍑犱綍鐩稿叧鐨勬蹇...
绛旓細鎵浠ワ紝瀹炴暟鐭╅樀鐨鍏辫江杞疆鐭╁姛灏辨槸杞疆鐭╅樀锛屽鏁扮煩闃电殑鍏辫江杞疆鐭╅樀灏辨槸涓婇潰鎵璇寸殑琛屽垪浜掓崲鍚庢瘡涓厓绱犲彇鍏辫江銆傞棶棰樹簩锛氭庝箞鍐欏嚭杩欎釜鐭╅樀鐨勫叡杞煩闃靛厛杞疆鍐嶅姣忎釜鍏冪礌鍙栧叡杞.杞疆鍚庯細[-鈭2i4 -4鈭2i]鍐嶅彇鍏辫江锛歔鈭2i4 -4-鈭2i]闂涓夛細澶嶆暟鐭╅樀A鐨勫叡杞煩闃靛簲璇ユ庝箞绠楃浜岀鏄爣鍑瀹氫箟锛岄氬父璁板仛A...
