矩阵AH(H在A的右上角)是什么意思？ 矩阵右上角有个H，这是什么矩阵呢？（有个T是转置，有个H是什...
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A的共轭转置矩阵
绛旓細杩欐牱鐨勫垎瑙ｅ氨绉颁綔M鐨勫寮傚煎垎瑙ｃ偽ｅ瑙掔嚎涓婄殑鍏冪礌危i,i鍗充负M鐨勫寮傚 銆傚父瑙佺殑鍋氭硶鏄皢濂囧紓鍊肩敱澶ц屽皬鎺掑垪銆傚姝のｄ究鑳界敱M鍞竴纭畾浜嗐 涓涓鏂圭殑澶嶅肩煩闃电О涓篐ermitian鐭╅樀锛岃嫢A=AH鍗冲叾鍏冪礌,鎹㈣█涔婬ermitian鐭╅樀鏄涓绉嶅鍏辫江瀵圭О鐭╅樀 .瀵逛竴涓疄鍊肩煩闃碉紝Hermitian鐭╅樀涓庡绉扮煩闃电瓑浠枫 Vandermonde...
绛旓細(conjugate transpose)锛孉鍙充笂鍔*.寮曠敤Kalman 1972 骞寸粰鍑虹殑璇佹槑銆傝A鐨杞疆涓篈'(1)AGA=A , (2) GAG=G , (3) (AG)'=AG ,(4)(GA)'=GA 鍋囪鍙︽湁 H 婊¤冻(1) 锝 (4) , 娉ㄦ剰 A=AGA=(AGA)G(AGA),H= HAH = H(AGAGAGA)H = (HA)(GA)G(AG)(AH)=(HA)'(GA)'G(AG)'...
绛旓細璋辫寖鏁帮紝鍗矨^H*A鐗瑰緛鍊嘉籭涓渶澶ц呂1鐨勫钩鏂规牴锛屽叾涓瑼H涓A鐨杞疆鍏辫江鐭╅樀銆傚叕寮忥細鈺慉鈺2 = A鐨勬渶澶у寮傚 = (max{ 位i(AH*A) }) 1/2 銆傚叾浠栧父鐢ㄧ殑涓绉嶇p-鑼冩暟鎺ㄥ鍑虹殑鐭╅樀鑼冩暟锛1-鑼冩暟锛氣晳A鈺1 = max{ 鈭憒ai1|锛屸垜|ai2|锛屸︹︼紝鈭憒ain| } 锛堝垪鍜岃寖鏁帮紝A姣忎竴鍒楀厓绱犵粷瀵...
绛旓細绛変环鍛介1锛氳嫢A鏄箓绛夌煩闃碉紝鍒欎笌A鐩镐技鐨勪换鎰鐭╅樀鏄骞傜瓑鐭╅樀锛涚瓑浠峰懡棰2锛氳嫢A鏄箓绛夌煩闃碉紝鍒A鐨凙H銆丄T銆丄*銆丒-AH銆丒-AT閮芥槸骞傜瓑鐭╅樀锛涚瓑浠峰懡棰3锛氳嫢A鏄箓绛夌煩闃碉紝A鐨刱娆″箓浠嶆槸骞傜瓑鐭╅樀銆傜敱浜庡箓绛夌煩闃垫墍鍏锋湁鐨勮壇濂芥ц川鍙婂叾瀵瑰悜閲忕┖闂寸殑鍒掑垎锛屽箓绛鐭╅樀鍦鍙瑙掑寲鐭╅樀鐨勫垎瑙ｄ腑鍏锋湁閲嶈鐨勪綔鐢紝鍚屾椂涔熶负...
绛旓細鐭╅樀鏄楂樼瓑浠ｆ暟瀛︿腑鐨勫父瑙佸伐鍏凤紝涔熷父瑙佷簬缁熻鍒嗘瀽绛夊簲鐢ㄦ暟瀛﹀绉戜腑銆傚湪鐗╃悊瀛︿腑锛岀煩闃典簬鐢佃矾瀛︺佸姏瀛︺佸厜瀛﹀拰閲忓瓙鐗╃悊涓兘鏈夊簲鐢紱璁＄畻鏈虹瀛︿腑锛屼笁缁村姩鐢诲埗浣滀篃闇瑕佺敤鍒扮煩闃点 鐭╅樀鐨杩愮畻鏄暟鍊煎垎鏋愰鍩熺殑閲嶈闂銆傚皢鐭╅樀鍒嗚В涓虹畝鍗曠煩闃电殑缁勫悎鍙互鍦ㄧ悊璁哄拰瀹為檯搴旂敤涓婄畝鍖栫煩闃电殑杩愮畻銆傚涓浜涘簲鐢ㄥ箍娉涜屽舰寮...
绛旓細{ 位i(AH*A) }) 1/2 (璋辫寖鏁,鍗矨^H*A鐗瑰緛鍊嘉籭涓渶澶ц呂1鐨勫钩鏂规牴,鍏朵腑AH涓A鐨杞疆鍏辫江鐭╅樀);鈭-鑼冩暟:鈺慉鈺戔垶 = max{ 鈭憒a1j|,鈭憒a2j|,...,鈭憒amj| } (琛屽拰鑼冩暟,A姣忎竴琛屽厓绱犵粷瀵瑰间箣鍜岀殑鏈澶у)(鍏朵腑鈭憒a1j| 涓虹涓琛屽厓绱犵粷瀵瑰肩殑鍜,鍏朵綑绫讳技);鍏跺畠鐨刾-鑼冩暟鍒欐病鏈夊緢绠鍗曠殑...
绛旓細||w||琛ㄧず涓2-鑼冩暟銆傚锛寃鏄竴涓猲缁村垪鍚戦噺锛寃=(w1,w2,...,wn)';||w||=w'w銆備簩鑼冩暟鎸鐭╅樀A鐨2鑼冩暟锛屽氨鏄疉鐨勮浆缃叡杞煩闃典笌鐭╅樀A鐨勭Н鐨勬渶澶х壒寰佹牴鐨勫钩鏂规牴鍊硷紝鏄寚绌洪棿涓婁袱涓悜閲忕煩闃电殑鐩寸嚎璺濈銆傜被浼间簬姹傛鐩樹笂涓ょ偣闂寸殑鐩寸嚎璺濈銆傝寖鏁(norm)鏄暟瀛︿腑鐨勪竴绉嶅熀鏈蹇点傚湪娉涘嚱鍒嗘瀽涓紝瀹...
绛旓細A 鐨鐗瑰緛鍊间负 1,1,2 (A-E)x=0 鐨勫熀纭瑙ｇ郴涓 (1,0,0)^T,(0,1,2)^T (A-2E)x=0 鐨勫熀纭瑙ｇ郴涓(4,-2,-3)浠 H= 1 0 4 0 1 -2 0 2 -3 鍒橦鍙,涓 H^-1AH = diag(1,1,2)
绛旓細鍏蜂綋鍥炵瓟濡傚浘锛氳嫢A涓烘柟闃碉紝涓擜²=A锛屽垯A绉颁负骞傜瓑鐭╅樀銆備緥濡傦紝鏌愯鍏ㄤ负1鑰屽叾浠栬鍏ㄤ负0鐨勬柟闃垫槸骞傜瓑鐭╅樀銆傚疄闄呬笂锛岀敱Jordan鏍囧噯鍨嬫槗鐭ワ紝鎵鏈夊箓绛夌煩闃甸兘鐩镐技浜庡瑙掑厓鍏ㄤ负0鎴1鐨勫瑙掗樀銆
绛旓細绉颁负A鐨鐗瑰緛澶氶」寮忥紝璁¦(位)=|位E-A|锛屾槸涓涓狿涓婄殑鍏充簬位鐨刵娆″椤瑰紡锛孍鏄崟浣鐭╅樀銆¦(位)=|位E-A|=位+a1位+鈥+an= 0鏄竴涓猲娆′唬鏁版柟绋嬶紝绉颁负A鐨勭壒寰佹柟绋嬨傜壒寰佹柟绋¦(位)=|位E-A|=0鐨勬牴(濡傦細位0)绉颁负A鐨勭壒寰佹牴(鎴栫壒寰佸)銆俷娆′唬鏁版柟绋嬪湪澶嶆暟鍩熷唴鏈変笖浠...
