矩阵列向量组的任意极大无关组所含的向量个数等于它的梯矩阵所有主列的向量数? 向量个数是指什么? 向量组中极大线性无关组如何找?是如何定义的?

\u4e3a\u4ec0\u4e48\u6781\u5927\u65e0\u5173\u7ec4\u4e2d\u5411\u91cf\u7684\u4e2a\u6570\u7b49\u4e8e\u7531\u5411\u91cf\u7ec4\u6784\u6210\u7684\u77e9\u9635\u7684\u79e9?

\u77e9\u9635\u4e0d\u5c31\u662f\u7531\u5217\uff08\u884c\uff09\u5411\u91cf\u7ec4\u6210\u7684\u5417\uff0c\u77e9\u9635\u770b\u6210\u662f\u5411\u91cf\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u96c6\u5408\uff0c\u5217\u5411\u91cf\u770b\u6210\u662f\u5143\u7d20\uff0c\u77e9\u9635\u7684\u79e9\u4e0d\u662f\u5316\u7b80\u77e9\u9635\u5f97\u5230\u7684\u5417\uff0c\u521d\u7b49\u884c\u53d8\u6362\u53ef\u4ee5\u770b\u505a\u662f\u628a\u5411\u91cf\u7684\u540c\u4e00\u4e2a\u4f4d\u7f6e\u5316\u4e3a0\uff0c\u5c31\u548c\u65b9\u7a0b\u7ec4\u5316\u7b80\u4e0d\u4e5f\u662f\u628a\u4e0d\u540c\u65b9\u7a0b\u7ec4\u7684\u672a\u77e5\u91cf\u6d88\u53bb\u5417\uff0c\u6700\u540e\u5316\u7b80\u5f97\u5230\u7684\u6700\u7b80\u5f62\u5c31\u662f\u8fd9\u4e2a\u77e9\u9635\u6240\u4ee3\u8868\u7684\u96c6\u5408\u7a7a\u95f4\u7684\u4e00\u4e2a\u6807\u51c6\u6b63\u4ea4\u57fa\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u77e9\u9635\u4e2d\u7684\u4efb\u610f\u7684\u5411\u91cf\u90fd\u53ef\u4ee5\u7531\u8fd9\u7ec4\u6807\u51c6\u6b63\u4ea4\u57fa\u8868\u793a\uff0c\u90a3\u8fd9\u4e2a\u6807\u51c6\u6b63\u4ea4\u57fa\u4e0d\u5c31\u662f\u6781\u5927\u65e0\u5173\u7ec4\u7684\u5b9a\u4e49\u561b\uff0c\u90a3\u4e0d\u5c31\u76f8\u7b49\u4e86\u561b

\u9996\u5148\u628a\u8fd9\u4e2a\u5411\u91cf\u7ec4\u5316\u4e3a\u884c\u6700\u7b80\u5f62\u5373\u9636\u68af\u77e9\u9635\uff0c\u627e\u5230\u6bcf\u5217\u975e\u96f6\u5143\u7d20\u5373\u53ef\uff0c\u4f8b\u5982\uff1a
a1 a2 a3 a4
1 0 1 0
0 1 1 0
0 0 0 1
0 0 0 0
\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u5373\u4e3a\uff1aa1\uff0ca2\uff0ca4\uff1ba2\uff0ca3\uff0ca4\uff1ba1\uff0ca3\uff0ca4\uff1ba1\uff0ca2\uff0ca3\u4e0d\u662f\u6781\u5927\u65e0\u5173\u7ec4\u3002
\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u662f\u7ebf\u6027\u7a7a\u95f4\u7684\u57fa\u5bf9\u5411\u91cf\u96c6\u7684\u63a8\u5e7f\u3002\u8bbeV\u662f\u57dfP\u4e0a\u7684\u7ebf\u6027\u7a7a\u95f4\uff0cS\u662fV\u7684\u5b50\u96c6\u3002\u82e5S\u7684\u4e00\u90e8\u5206\u5411\u91cf\u7ebf\u6027\u65e0\u5173\uff0c\u4f46\u5728\u8fd9\u90e8\u5206\u5411\u91cf\u4e2d\uff0c\u52a0\u4e0aS\u7684\u4efb\u4e00\u5411\u91cf\u540e\u90fd\u7ebf\u6027\u76f8\u5173\uff0c\u5219\u79f0\u8fd9\u90e8\u5206\u5411\u91cf\u662fS\u7684\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u3002
V\u4e2d\u5b50\u96c6\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u4e0d\u662f\u60df\u4e00\u7684\uff0c\u4f8b\u5982\uff0cV\u7684\u57fa\u90fd\u662fV\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u3002\u5b83\u4eec\u6240\u542b\u7684\u5411\u91cf\u4e2a\u6570\uff08\u57fa\u6570\uff09\u76f8\u540c\u3002V\u7684\u5b50\u96c6S\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u6240\u542b\u5411\u91cf\u7684\u4e2a\u6570\uff08\u57fa\u6570\uff09\uff0c\u79f0\u4e3aS\u7684\u79e9\u3002

\u57fa\u672c\u6027\u8d28\uff1a
\uff081\uff09\u53ea\u542b\u96f6\u5411\u91cf\u7684\u5411\u91cf\u7ec4\u6ca1\u6709\u6781\u5927\u65e0\u5173\u7ec4\uff1b
\uff082\uff09\u4e00\u4e2a\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u7ec4\u7684\u6781\u5927\u65e0\u5173\u7ec4\u5c31\u662f\u5176\u672c\u8eab\uff1b
\uff083\uff09\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u5bf9\u4e8e\u6bcf\u4e2a\u5411\u91cf\u7ec4\u6765\u8bf4\u5e76\u4e0d\u552f\u4e00\uff0c\u4f46\u662f\u6bcf\u4e2a\u5411\u91cf\u7ec4\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u90fd\u542b\u6709\u76f8\u540c\u4e2a\u6570\u7684\u5411\u91cf\uff1b
\uff084\uff09\u9f50\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3\u5411\u91cf\u7684\u6781\u5927\u65e0\u5173\u7ec4\u4e3a\u57fa\u7840\u89e3\u7cfb\u3002
\uff085\uff09\u4efb\u610f\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u90fd\u4e0e\u5411\u91cf\u7ec4\u672c\u8eab\u7b49\u4ef7\u3002
\uff086\uff09\u4e00\u5411\u91cf\u7ec4\u7684\u4efb\u610f\u4e24\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u90fd\u662f\u7b49\u4ef7\u7684\u3002
\uff087\uff09\u82e5\u4e00\u4e2a\u5411\u91cf\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u5411\u91cf\u90fd\u80fd\u7528\u53e6\u4e00\u4e2a\u5411\u91cf\u7ec4\u4e2d\u7684\u5411\u91cf\u7ebf\u6027\u8868\u51fa\uff0c\u5219\u524d\u8005\u6781\u5927\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u7ec4\u7684\u5411\u91cf\u4e2a\u6570\u5c0f\u4e8e\u6216\u7b49\u4e8e\u540e\u8005\u3002

任意极大无关组所含的向量个数,其实就是矩阵的秩
主列,就是只含1个1,其余行为0的列向量

  • 濡備綍姹鐭╅樀鐨勬瀬澶ф棤鍏崇粍?
    绛旓細鍏堟妸閭e嚑涓悜閲忎互鍒楀悜閲鐨勫舰寮忓啓鎴愪竴涓鐭╅樀锛岀劧鍚庢眰杩欎釜鐭╅樀鐨勭З锛屽洜涓烘瀬澶ф棤鍏崇粍涓悜閲忕殑涓暟灏辨槸鐭╅樀鐨勭З銆傝姹傜煩闃电殑绉╁綋鐒惰鍏堟妸鐭╅樀鍖栨垚琛岀畝鍖栭樁姊瀷鐭╅樀锛岀劧鍚庣湅鐪嬪叾涓殑鍗曚綅闃甸儴鍒嗗搴斿摢鍑犱釜鍚戦噺锛岃繖鍑犱釜鍚戦噺渚挎槸鏋佸ぇ鏃犲叧缁勭殑鎴愬憳銆備緥瀛愬涓嬶細姹俛1=(-1,-1,0,0)T锛宎2=(1,2,1,-2)T锛...
  • 濡備綍姹鐭╅樀鐨勬瀬澶ф棤鍏崇粍?
    绛旓細1銆佹妸鍚戦噺浠鍒楀悜閲褰㈠紡缁勬垚鐭╅樀锛堟彁闂浘涓墍鍐欑殑鏄鍒楀紡| |锛屼笉鏄煩闃礫 ],浜岃呭繀椤诲尯鍒嗭級锛2銆佺煩闃靛彉鎹㈠寲闃舵鍨嬶紝鍖栨渶绠褰紝姹傚嚭鐭╅樀鐨绉㏑(A),鍗抽樁姊樁鏁帮紱3銆鏈澶ф棤鍏崇粍鍚戦噺琛ㄧず锛屼袱绉嶆柟娉曪紝涓锛岀洿鎺ヨ瀵熷叧绯诲啓鍑哄叧绯伙紝浜岋紝鍒╃敤鏈绠褰㈢煩闃垫渶鍚庝竴鍒楃殑绯绘暟鍊硷紙a,b,c锛夛紝伪4=a伪1+b伪2+c...
  • 姹鐭╅樀A鍒楀悜閲忕粍鐨涓涓瀬澶ф棤鍏冲苟鎶婁笉灞炰簬鏃犲叧缁勭殑鍒楀悜閲忕敤鏋佸ぇ鏃犲叧缁...
    绛旓細r4-3r1 0 0 0 1 -3 1 0 -1 0 4 0 1 -1 0 3 0 0 0 0 0 浜ゆ崲琛 1 0 -1 0 4 0 1 -1 0 3 0 0 0 1 -3 0 0 0 0 0 伪1,伪2,伪4 鏄疉鐨鍒楀悜閲忕粍鐨涓涓鏋佸ぇ鏃犲叧缁.伪3 = -伪1-伪2 伪5 = 4伪1+3伪2-3伪4 ...
  • 鎬庢牱姹鐭╅樀涓鍚戦噺缁勬垨鍒楀悜閲忕粍鐨勬瀬澶ф棤鍏崇粍
    绛旓細灏鍚戦噺缁鍐欐垚鐭╅樀鐨褰㈠紡锛岀劧鍚庡寲琛屾渶绠褰紝鎴栬呴樁姊瀷 鍗冲彲鍙戠幇鍏朵腑鏁扮洰鏈澶х殑绾挎ф棤鍏崇殑鍚戦噺缁勶紝浣滀负涓涓鏋佸ぇ鏃犲叧缁
  • 鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁鏈夊摢浜涙ц川?
    绛旓細鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁婊¤冻2涓潯浠 1. 鑷韩绾挎ф棤鍏 2. 鍚戦噺缁勪腑鎵鏈夊悜閲忓彲鐢卞畠绾挎ц〃绀 渚嬮鐨勮В娉:鏋勯鐭╅樀 (a1,a2,a3,a4), 瀵瑰畠鐢ㄨ鍙樻崲鍖栨垚姊煩闃 闈為浂琛岀殑棣栭潪闆跺厓鎵鍦ㄧ殑鍒楀搴旂殑鍚戦噺灏辨槸涓涓瀬澶ф棤鍏崇粍 5 4 1 3 2 1 1 4 -3 -2 -1 -1 1 3 -2 2 鎴戠敤杞欢鍖栨垚...
  • 鍚戦噺缁涓鐨勬瀬澶绾挎鏃犲叧缁鏈変粈涔堢敤?
    绛旓細1. 灏鍚戦噺缁鎺掑垪鎴愮煩闃靛舰寮忥細灏嗗悜閲忔寜鍒楃粍鎴愪竴涓煩闃碉紝姣忎釜鍚戦噺浣滀负鐭╅樀鐨涓鍒椼2. 瀵圭煩闃佃繘琛岃鍙樻崲锛氫娇鐢ㄩ珮鏂秷鍏冩硶鎴栧叾浠栬鍙樻崲鏂规硶锛屽皢鐭╅樀杞寲涓鸿绠鍖栭樁姊舰寮忥紙REF锛夋垨琛屾渶绠褰㈠紡锛圧REF锛夈3. 璇嗗埆鏋佸ぇ绾挎鏃犲叧缁锛氳瀵熷彉鎹㈠悗鐨勭煩闃点傛瀬澶х嚎鎬ф棤鍏崇粍鏄寚鍦≧EF鎴朢REF涓紝棣栨鍑虹幇鐨勯潪闆惰鎵...
  • 鍩虹瑙g郴鍜岀郴鏁鐭╅樀涓鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁涔嬮棿鏈変粈涔堣仈绯?鎬庝箞鍖哄垎鍟...
    绛旓細灏鐭╅樀鍒濈瓑琛屽彉鍖栧悗鍖栦负闃舵褰紝鏋佸ぇ鍚戦噺缁勫氨鏄夋嫨闈0棣栭」鎵鍦ㄥ垪锛屼负鏃犲叧缁勩傚熀纭瑙g郴灏辨槸鏋佸ぇ鏃犲叧缁 鏄寚鍩虹瑙g郴 鏄 鐢盇x=0 鐨勫叏閮ㄨВ鏋勬垚鐨 鍚戦噺缁 鐨 鏋佸ぇ鏃犲叧缁 1,0,2,2 0,1,1,0 0,0,0,3 0,0,0,0 杩欓噷鐨勮嚜鐢辨湭鐭ラ噺搴旇閫 x3 x4 = 0 鏄埍绾︽潫鐨 鐭╅樀搴旇繘涓姝ュ寲涓鸿鏈...
  • 鎬庝箞姹鐭╅樀鐨勬渶澶ф棤鍏崇粍?
    绛旓細鍙互閲囩敤鐢婚樁姊殑鏂规硶锛屽浘涓凡缁忔爣鍑烘潵浜嗐傜劧鍚庡湪姣忎釜鍙伴樁涓婁笂鎵句竴涓悜閲忥紝鏈鍚庣粍鎴愮殑鍚戦噺缁灏辨槸鏋佸ぇ绾挎鏃犲叧缁銆傝繖閲岀涓涓彴闃朵笂鎵句竴涓紝鍙湁伪1锛涚浜屼釜鍙伴樁涓婃壘涓涓紝伪2銆佄3銆佄4涓変釜閲岄潰浠绘剰鎵句竴涓潎鍙傛墍浠ユ渶鍚庢瀬澶х嚎鎬ф棤鍏崇粍鍙互鏄細伪1,伪2锛屾垨伪1,伪3锛屾垨伪1,伪4銆
  • 鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁鎬庝箞姹?
    绛旓細1銆佸皢鍚戦噺缁勭煩闃杩涜鍒濈瓑琛屽彉鎹紝寰楀嚭伪1锛屛2锛屛3鏄鏋佸ぇ绾挎鏃犲叧缁锛岀劧鍚庤В鏂圭▼伪4=k1伪1+k2伪2+k3伪3鍗冲彲寰楀嚭锛2銆佸皢鍚戦噺缁勭煩闃佃繘琛屽垵绛夎鍙樻崲锛岄氳繃瑙f柟绋嬬粍锛屾眰鍑虹郴鏁帮紟涓句緥锛氭湁浠ヤ笅鍚戦噺锛氾紙5 2 -3 1锛塗 锛4 1 -2 3锛塗 锛1 1 -1 -2锛塗 锛3 4 -1 2锛塗 鎸鍒楀悜閲...
  • 鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁婊¤冻浠涔堟潯浠?
    绛旓細鍚戦噺缁勭殑鏋佸ぇ鏃犲叧缁婊¤冻2涓潯浠讹細1銆佽嚜韬嚎鎬ф棤鍏炽2銆佸悜閲忕粍涓墍鏈夊悜閲忓彲鐢卞畠绾挎ц〃绀恒備緥棰樼殑瑙f硶锛氭瀯閫鐭╅樀 (a1锛宎2锛宎3锛宎4)锛屽瀹冪敤琛屽彉鎹㈠寲鎴愭鐭╅樀銆傞潪闆惰鐨勯闈為浂鍏冩墍鍦ㄧ殑鍒楀搴旂殑鍚戦噺灏辨槸涓涓瀬澶ф棤鍏崇粍銆5 4 1 3 2 1 1 4 -3 -2 -1 -1 1 3 -2 2 鍖栨垚浜嗚绠鍖栨鐭╅樀...
  • 扩展阅读:极大无关组求解步骤 ... 行向量组的最大无关组 ... 极大无关组怎么找 ... 求最大无关组 ... 极大无关组的个数与秩 ... 两个不同的极大无关组 ... 最大无关特征向量组 ... 怎么判断最大无关组 ... 怎么看哪个是极大无关组 ...

    本站交流只代表网友个人观点,与本站立场无关
    欢迎反馈与建议,请联系电邮
    2024© 车视网