矩阵范数有哪些 什么是矩阵的范数
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(1). \u6b63\u5b9a\u6027\uff1aA \u2260 0\uff0c\u5219 || A || > 0\uff1b
(2). \u7ebf\u6027\u6027\uff1at \u2208 R\uff0c\u5219 || t A || = |t| || A ||\uff1b
(3). \u4e09\u89d2\u4e0d\u7b49\u5f0f\uff1a|| A + B || <= || A || + || B ||.
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1范数，2范数，无穷范数，三种
绛旓細姣斿甯哥敤鐨凢robenius鑼冩暟(涔熷彨Euclid鑼冩暟锛岀畝绉癋-鑼冩暟鎴栬匛-鑼冩暟)锛氣晳A鈺慒= ( 鈭戔垜 aij^2 )^1/2 (A鍏ㄩ儴鍏冪礌骞虫柟鍜岀殑骞虫柟鏍)銆傚鏄撻獙璇丗-鑼冩暟鏄浉瀹圭殑锛屼絾褰搈in{m,n}>1鏃禙-鑼冩暟涓嶈兘鐢卞悜閲忚寖鏁拌瀵(||E11+E22||F=2>1)銆傚彲浠ヨ瘉鏄庝换涓绉鐭╅樀鑼冩暟鎬绘湁涓庝箣鐩稿鐨勫悜閲忚寖鏁般
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绛旓細鐭╅樀A鐨2鑼冩暟灏辨槸 A涔樹互A鐨勮浆缃煩闃电壒寰佹牴 鏈澶у肩殑寮鏍瑰彿濡侫={ 1 -2-3 4 }閭ｄ箞A鐨2鑼冩暟灏辨槸锛15+221^1/2)^1/2 浜 涓鑼冩暟鍜屼簩鑼冩暟鏈鍟ュ尯鍒細1銆佷笉鍚岀殑鍚箟锛1-鑼冩暟鏄寚鍚戦噺锛堢煩闃碉級涓潪闆跺厓绱犵殑涓暟锛2-鑼冩暟鏄寚绌洪棿涓袱涓悜閲忕煩闃典箣闂寸殑鐩寸嚎璺濈銆2銆佷笉鍚屾柟娉曪細1-鑼冩暟a 1=鏈...
绛旓細绾挎т唬鏁颁腑 ||a|| 鏄寚鍚戦噺a鐨勯暱搴 ||a|| = 鈭(a,a) = 鈭歛^Ta 鍏朵腑 (a,a) 鏄痑涓巃鐨勫唴绉,鏄痑鐨勫悇鍒嗛噺鐨勫钩鏂逛箣鍜 濡俛=锛圶1,X2,X3锛,鍒檤|a||=鈭歑1^2+X2^2+X3^3
绛旓細甯哥敤鍚戦噺鑼冩暟鐨勫畾涔夌畝鍗曚竴浜涳紝灏辨槸鎵鏈夊厓绱犵粷瀵瑰肩殑F娆℃柟鐩稿姞鍐嶅紑F娆℃柟锛屽父鐢鐭╅樀鑼冩暟鏈1鑼冩暟2鑼冩暟鍜屾棤绌疯寖鏁帮紝1鑼冩暟灏辨槸鍒楄寖鏁帮紝鐭╅樀鐨勫悇鍒楃粷瀵瑰间箣鍜岀殑鏈澶у硷紝鏃犵┓鑼冩暟灏辨槸琛岃寖鏁帮紝鐭╅樀鍚勮鐨勭粷瀵瑰间箣鍜岀殑鏈澶у硷紝2鑼冩暟灏辨槸闀ㄨ寖鏁帮紝瀹冨湪鐭╅樀涓嶄负0鐨勬椂鍊欑瓑浜庣煩闃电殑璋卞崐寰勩
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绛旓細涓鑸鐭╅樀鑼冩暟闄や簡姝ｅ畾鎬э紝榻愭鎬у拰涓夎涓嶇瓑寮忎箣澶栵紝杩樿瀹氬叾蹇呴』婊¤冻鐩稿鎬э細鈺慩Y鈺戔墹鈺慩鈺戔晳Y鈺戙傛墍浠ョ煩闃佃寖鏁伴氬父涔熺О涓虹浉瀹硅寖鏁般 鎵╁睍璧勬枡 濡傛灉鈺懧封晳伪鏄浉瀹硅寖鏁帮紝涓斾换浣曟弧瓒斥晳路鈺懳测墹鈺懧封晳伪鐨勮寖鏁扳晳路鈺懳查兘涓嶆槸鐩稿鑼冩暟锛岄偅涔堚晳路鈺懳辩О涓烘瀬灏忚寖鏁般傚浜巒闃跺疄鏂归樀锛堟垨澶嶆柟闃碉級...
