列向量是什么意思 列向量是什么意思?
\u5411\u91cf\u5171\u9762\u662f\u4ec0\u4e48\u610f\u601d\u5171\u9762\u5b9a\u7406\u7684\u5b9a\u4e49\u4e3a\u80fd\u5e73\u79fb\u5230\u4e00\u4e2a\u5e73\u9762\u4e0a\u7684\u4e09\u4e2a\u5411\u91cf\u79f0\u4e3a\u5171\u9762\u5411\u91cf\u3002\u5171\u9762\u5411\u91cf\u5b9a\u7406\u662f\u6570\u5b66\u5b66\u79d1\u7684\u57fa\u672c\u5b9a\u7406\u4e4b\u4e00\u3002\u5c5e\u4e8e\u9ad8\u4e2d\u6570\u5b66\u7acb\u4f53\u51e0\u4f55\u7684\u6559\u5b66\u8303\u7574\u3002\u4e3b\u8981\u7528\u4e8e\u8bc1\u660e\u4e24\u4e2a\u5411\u91cf\u5171\u9762\uff0c\u8fdb\u800c\u8bc1\u660e\u9762\u9762\u5782\u76f4\u7b49\u4e00\u7cfb\u5217\u590d\u6742\u5b9a\u7406\u3002
\u63a8\u8bba1
\u8bbeOABC\u662f\u4e0d\u5171\u9762\u7684\u56db\u70b9 \u5219\u5bf9\u7a7a\u95f4\u4efb\u610f\u4e00\u70b9P \u90fd\u5b58\u5728\u552f\u4e00\u7684\u6709\u5e8f\u5b9e\u6570\u7ec4(x,y,z)
\u4f7f\u5f97OP=xOA+yOB+zOC {OP,OA,OB,OC\u5747\u8868\u793a\u5411\u91cf} \u8bf4\u660e\uff1a\u82e5x+y+z=1 \u5219PABC\u56db\u70b9\u5171\u9762 \uff08\u4f46PABC\u56db\u70b9\u5171\u9762\u7684\u65f6\u5019\uff0c\u82e5O\u5728\u5e73\u9762ABP\u5185\uff0c\u5219x+y+z\u4e0d\u4e00\u5b9a\u7b49\u4e8e1\uff0c\u5373x+y+z=1 \u662fP.A.B.C\u56db\u70b9\u5171\u9762\u7684\u5145\u5206\u4e0d\u5fc5\u8981\u6761\u4ef6\uff09
\u8bc1\u660e\uff1a
1\uff09\u552f\u4e00\u6027\uff1a
\u8bbe\u53e6\u6709\u4e00\u7ec4\u5b9e\u6570x',y',z' \u4f7f\u5f97OP=x'OA+y'OB+z'OC
\u5219\u6709xOA+yOB+zOC=x'OA+y'OB+z'OC
\u2234(x-x')OA+(y-y')OB+(z-z')OC=0
\u2235OA\u3001OB\u3001OC\u4e0d\u5171\u9762
\u2234x-x'=y-y'=z-z'=0\u5373x=x'\u3001y=y'\u3001z=z'
\u6545\u5b9e\u6570x,y,z\u662f\u552f\u4e00\u7684
2\uff09\u82e5x+y+z=1 \u5219PABC\u56db\u70b9\u5171\u9762\uff1a
\u5047\u8bbeOP=xOA+yOB+zOC\u4e14x+y+z=1 \u4e14PABC\u4e0d\u5171\u9762
\u90a3\u4e48z=1-x-y \u5219OP=xOA+yOB+OC-xOC-yOC
OP=OC+xCA+yCB(CP=xCA+yCB)
\u70b9P\u4f4d\u4e8e\u5e73\u9762ABC\u5185 \u4e0e\u5047\u8bbe\u4e2d\u7684\u6761\u4ef6\u77db\u76fe \u6545\u539f\u547d\u9898\u6210\u7acb
n\u7ef4\u5217\u5411\u91cf\u662fn\u884c1\u5217\uff0cn\u7ef4\u884c\u5411\u91cf\u662f1\u884cn\u5217\uff1b\u76f4\u89c2\u662f\uff0c\u5217\u5411\u91cf\u662f1\u5217\uff0c\u884c\u5411\u91cf\u662f1\u884c\u3002
n\u5143\u5411\u91cf\u7684\u52a0\u6cd5\uff0cP\u4e2d\u7684\u6570\u4e0en\u5143\u5411\u91cf\u7684\u6570\u91cf\u4e58\u6cd5(\u7b80\u79f0\u6570\u4e58)\u5b9a\u4e49\u4e3a\uff1a
(a1\uff0ca2\uff0c\u2026\uff0can)+(b1\uff0cb2\uff0c\u2026\uff0cbn)=(a1+b1\uff0ca2+b2\uff0c\u2026\uff0can+bn)\uff1b
c(a1\uff0ca2\uff0c\u2026\uff0can)=(ca1\uff0cca2\uff0c\u2026\uff0ccan)
(c\u2208P).
\u5206\u91cf\u90fd\u662f0\u7684n\u5143\u5411\u91cf(0\uff0c0\uff0c\u2026\uff0c0)\u79f0\u4e3a\u96f6\u5411\u91cf\uff0c\u8bb0\u4e3a0\u3002
\u6269\u5c55\u8d44\u6599
\u5411\u91cf\u7684\u6027\u8d28\uff1a
1\u3001\u4e00\u4e2am\u00d7n\u77e9\u9635\u7684\u5217\u7a7a\u95f4\u4e00\u5b9a\u5728R^m\u4e2d\u3002
2\u3001\u4e00\u4e2am\u00d7n\u77e9\u9635\u7684\u5217\u7a7a\u95f4\u5982\u679c\u662fR\uff0c\u82e5m\u7b49\u4e8en,\u90a3\u4e48\u8fd9\u4e2a\u77e9\u9635\u4e00\u5b9a\u53ef\u9006\u3002
\u5176\u5b9e\u77e9\u9635A\u4e58\u5411\u91cfx\u5c31\u662f\u4e00\u4e2a\u5c06\u5411\u91cfx\u7531A\u7684\u884c\u7a7a\u95f4\u5411A\u7684\u5217\u7a7a\u95f4\u6620\u5c04\u7684\u8fd0\u7b97\u3002
\u77e9\u9635\u4e58\u6cd5\u662f\u628a\u6bcf\u4e00\u4e2a\u77e9\u9635\u7684\u5217\u5411\u91cf\u540c\u53e6\u4e00\u4e2a\u77e9\u9635\u7684\u6bcf\u884c\u5411\u91cf\u76f8\u4e58\u3002\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u7684\u70b9\u79ef\u5c31\u662f\u628a\u5176\u4e2d\u4e00\u4e2a\u5217\u5411\u91cf\u7684\u8f6c\u7f6e\u4e0e\u53e6\u4e00\u4e2a\u5217\u5411\u91cf\u76f8\u4e58\u3002
┌a┐
│b│
│·│ 叫“列向量”.[竖着排的“有次序的n数组”]
│·│
│·│
└c┘
绛旓細涓夌淮鍗曚綅鍒楀悜閲忥細e1{1锛0锛0}, e2{0, 1, 0}, e3 {0, 0 , 1}銆傚悜閲廵1锛宔2锛宔3 鐨勮浆缃负琚О涓3缁村崟浣嶅垪鍚戦噺銆傜敤[ ]鎷捣鏉ュ氨琛ㄧず涓涓笁缁村垪鍚戦噺銆傚湪绾挎т唬鏁颁腑锛鍒楀悜閲忔槸涓涓 n脳1 鐨勭煩闃碉紝鍗崇煩闃电敱涓涓惈鏈塶涓厓绱犵殑鍒楁墍缁勬垚锛氬垪鍚戦噺鐨勮浆缃槸涓涓鍚戦噺锛屽弽涔嬩害鐒躲傛墍鏈夌殑鍒楀悜閲...
绛旓細涓夌淮鍗曚綅鍒楀悜閲忥細e1{1锛0锛0}锛宔2{0, 1, 0}锛宔3 {0, 0 , 1}銆傚悜閲廵1锛宔2锛宔3 鐨勮浆缃负琚О涓3缁村崟浣嶅垪鍚戦噺銆備笁缁村崟浣嶅垪鍚戦噺锛歟1{1锛0锛0}, e2{0, 1, 0}, e3 {0, 0 , 1}銆傚悜閲廵1锛宔2锛宔3 鐨勮浆缃负琚О涓3缁村崟浣嶅垪鍚戦噺銆傚湪绾挎т唬鏁颁腑锛鍒楀悜閲忔槸涓涓 n脳1 鐨勭煩闃碉紝鍗...
绛旓細鎵鏈夎鏋勬垚鐨勫悜閲忕殑鏁翠綋绉颁负涓涓鍚戦噺缁 鍒楀悜閲缁勬寚鐨勬槸鐭╅樀姣忓垪鏋勬垚涓涓悜閲,鎵鏈夊垪鏋勬垚鐨勫悜閲忕殑鏁翠綋绉颁负涓涓垪鍚戦噺缁 渚嬪锛 缁欎綘涓涓煩闃礎 A = 1 2 3 4 5 6 鍒橝鐨勮鍚戦噺缁勪负: (1,2,3), (4,5,6)A鐨勫垪鍚戦噺缁勪负: (1,4)',(2,5)', (3,6)'
绛旓細n缁鍚戦噺鏄涓涓滄湁娆″簭鐨刵鏁扮粍鈥,锛坅,b,鈥︹︼紝c锛夊彨鈥滆鍚戦噺鈥濄傗攲a鈹 鈹俠鈹 鈹偮封攤 鍙鍒楀悜閲鈥濄俒绔栫潃鎺掔殑鈥滄湁娆″簭鐨刵鏁扮粍鈥漖鈹偮封攤 鈹偮封攤 鈹攃鈹
绛旓細鍥涚淮鍒楀悜閲忔槸绾挎т唬鏁颁腑鐨勪竴涓噸瑕佹蹇点傛垜浠煡閬擄紝鍚戦噺閫氬父琚敤鏉ヨ〃绀虹┖闂翠腑鐨勪竴涓偣鎴栬呯澶达紝瀹冪敱涓缁勬湁搴忕殑鏁板肩粍鎴愩傝屽洓缁村垪鍚戦噺鐢卞洓涓暟鍊肩粍鎴愶紝閫氬父鐢ㄦ潵琛ㄧず鍥涚淮绌洪棿涓殑涓涓偣銆佺澶存垨鑰呭叾浠栧嚑浣曞疄浣撱傚洓缁村垪鍚戦噺鍦ㄧ墿鐞嗗鍜屽伐绋嬪涓湁骞挎硾鐨勫簲鐢ㄣ備緥濡傦紝鐭㈤噺鍦烘槸鎸囧湪鏃剁┖涓瘡涓偣涓婂畾涔夌殑鐭㈤噺銆
绛旓細涓夌淮鍒楀悜閲灏辨槸涓涓笁琛屼竴鍒楃殑鐭╅樀锛屽畠鐨勭З涓嶈秴杩囧垪鏁帮紝涔熷氨鏄皬浜庣瓑浜1銆傛牴鎹悜閲忕粍鐨勭З鍙互鎺ㄥ嚭涓浜涚嚎鎬т唬鏁颁腑姣旇緝鏈夌敤鐨勫畾鐞嗭細鍚戦噺缁勎1锛屛2锛屄仿仿凤紝伪s绾挎ф棤鍏崇瓑浠蜂簬R{伪1锛屛2锛屄仿仿凤紝伪s}=s銆傝嫢鍚戦噺缁勎1锛屛2锛屄仿仿凤紝伪s鍙鍚戦噺缁勎1锛屛2锛屄仿仿凤紝尾t绾挎ц〃鍑猴紝鍒...
绛旓細涓夎涓鍒楃殑鐭╅樀鍚戦噺涓嶅叡闈備笁缁村垪鍚戦噺灏辨槸涓涓笁琛屼竴鍒楃殑鐭╅樀锛岀З涓嶈秴杩囧垪鏁帮紝绾挎ф棤鍏冲嚑浣曟剰涔夋槸涓変釜鍚戦噺涓嶅叡闈紝涓夌淮绾挎ф棤鍏崇殑鍒楀悜閲忔槸鎰忔鏄笁琛屼竴鍒楃殑鐭╅樀鍚戦噺涓嶅叡闈傚湪鏁板涓紝鍚戦噺鎸囧叿鏈夊ぇ灏忓拰鏂瑰悜鐨勯噺锛屽畠鍙互褰㈣薄鍖栧湴琛ㄧず涓哄甫绠ご鐨勭嚎娈点
绛旓細鍗曚綅姝ｄ氦鍒楀悜閲鎸囩殑鏄痻銆亂鍐呯Н涓0锛屽嵆x鐨勮浆缃箻y涓0锛岃屽叾鍒嗛噺骞虫柟鍜屼负1锛屾寚鐨勬槸鍗曚綅姝ｄ氦鍚戦噺銆傚湪涓夌淮鍚戦噺绌洪棿涓紝涓や釜鍚戦噺鐨勫唴绉鏋滄槸闆讹紝閭ｄ箞灏辫杩欎袱涓鍚戦噺鏄姝ｄ氦鐨勩傗滄浜ゅ悜閲忊濇槸涓涓暟瀛︽湳璇紝鎸囩偣绉负闆剁殑涓や釜鎴栧涓悜閲忋傚嚑浣曞悜閲忕殑姒傚康鍦ㄧ嚎鎬т唬鏁颁腑缁忕敱鎶借薄鍖栵紝寰楀埌鏇翠竴鑸殑鍚戦噺姒傚康銆...
绛旓細n缁鍒楀悜閲忔槸n琛1鍒楋紝n缁磋鍚戦噺鏄1琛宯鍒楋紱鐩磋鏄紝鍒楀悜閲忔槸1鍒楋紝琛屽悜閲忔槸1琛屻傝鍒楀紡鐨勫兼槸涓涓暟瀛楋紝琛ㄧず鍚戦噺鎵鍦ㄧ┖闂寸殑鍏冪礌澶у皬銆傛瘮濡傦紝鍦ㄥ钩闈㈢洿瑙掑潗鏍囩郴涓紝鏁翠釜骞抽潰鍙互鐢遍暱瀹藉潎涓1鐨勬柟鏍兼瀯鎴愶紝杩欎釜鏂规牸鐨勫ぇ灏忎负1銆傝繖涓柟鏍煎氨鏄钩闈㈢洿瑙掑潗鏍囩郴涓殑鍏冪礌锛屽ぇ灏忎负1銆傚垪鍚戦噺鐨勮浆缃槸涓涓鍚戦噺锛屽弽...
绛旓細鍏蜂綋鍐呭濡備笅锛欰鐨勫垪鍚戦噺鐨勬瀬澶ф棤鍏崇粍鍜孊鐨勫垪鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁勬瀯鎴愮殑鍚戦噺缁勶紝涓烘柟渚跨О鍏朵负鍚戦噺缁凜銆(A锛孊)鐨勫垪鍚戦噺缁勭瓑浠蜂簬鍚戦噺缁凜锛屾晠r(A,B)=r(C)銆侰涓竴鍏辨湁r(A)+r( B)涓悜閲忥紝鏁卹(C)<=r(A)+r( B)銆傛晠r(A锛孊)<=r(A)+r( B)銆傚湪绾挎т唬鏁颁腑锛鍒楀悜閲忔槸涓涓 n脳1 ...
