矩阵某一行乘相同的数，矩阵大小变不变啊？？为什么啊 矩阵每一行都乘一个数 矩阵会变化吗？
\u77e9\u9635\u7684\u4e00\u884c\u540c\u65f6\u4e58\u4e00\u4e2a\u6570\uff0c\u77e9\u9635\u4e0d\u53d8\u5417\u4e0d\u662f\uff01
\u6839\u636e\u300a\u77e9\u9635\u76f8\u7b49\u300b\u7684\u5b9a\u4e49\uff0c\u6b64\u65f6\u77e9\u9635\u3010\u4f1a\u3011\uff08\u4f46\u4e5f\u4e0d\u4e00\u5b9a\uff0c\u6bd4\u5982\u82e5\u90a3\u4e00\u884c\u4e58\u4ee5\u4e00\uff09\u6539\u53d8\u3002\u4f46\uff0c\u5404\u79cd\u300a\u521d\u7b49\u53d8\u6362\u300b\uff08\u5305\u62ec\u8fd9\u4e2a\uff09\u3010\u90fd\u3011\u4e0d\u6539\u53d8\u300a\u77e9\u9635\u7684\u79e9\u300b\u3002
\u4e00\u4e2a\u6570\u4e58\u4ee5\u77e9\u9635\uff0c\u77e9\u9635\u91cc\u9762\u7684\u6bcf\u4e2a\u6570\u90fd\u8981\u4e58\uff0c \u8fd9\u662f\u6052\u7b49\u8fd0\u7b97\u3002\u5728\u6570\u5b66\u4e2d\uff0c\u77e9\u9635\uff08Matrix\uff09\u662f\u4e00\u4e2a\u6309\u7167\u957f\u65b9\u9635\u5217\u6392\u5217\u7684\u590d\u6570\u6216\u5b9e\u6570\u96c6\u5408\uff0c\u6700\u65e9\u6765\u81ea\u4e8e\u65b9\u7a0b\u7ec4\u7684\u7cfb\u6570\u53ca\u5e38\u6570\u6240\u6784\u6210\u7684\u65b9\u9635\u3002\u8fd9\u4e00\u6982\u5ff5\u753119\u4e16\u7eaa\u82f1\u56fd\u6570\u5b66\u5bb6\u51ef\u5229\u9996\u5148\u63d0\u51fa\u3002
\u77e9\u9635\u662f\u9ad8\u7b49\u4ee3\u6570\u5b66\u4e2d\u7684\u5e38\u89c1\u5de5\u5177\uff0c\u4e5f\u5e38\u89c1\u4e8e\u7edf\u8ba1\u5206\u6790\u7b49\u5e94\u7528\u6570\u5b66\u5b66\u79d1\u4e2d\u3002\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u77e9\u9635\u4e8e\u7535\u8def\u5b66\u3001\u529b\u5b66\u3001\u5149\u5b66\u548c\u91cf\u5b50\u7269\u7406\u4e2d\u90fd\u6709\u5e94\u7528\uff1b\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\uff0c\u4e09\u7ef4\u52a8\u753b\u5236\u4f5c\u4e5f\u9700\u8981\u7528\u5230\u77e9\u9635\u3002
\u6269\u5c55\u8d44\u6599\u77e9\u9635\u5728\u7269\u7406\u5b66\u4e2d\u7684\u53e6\u4e00\u7c7b\u6cdb\u5e94\u7528\u662f\u63cf\u8ff0\u7ebf\u6027\u8026\u5408\u8c03\u548c\u7cfb\u7edf\u3002\u8fd9\u7c7b\u7cfb\u7edf\u7684\u8fd0\u52a8\u65b9\u7a0b\u53ef\u4ee5\u7528\u77e9\u9635\u7684\u5f62\u5f0f\u6765\u8868\u793a\uff0c\u5373\u7528\u4e00\u4e2a\u8d28\u91cf\u77e9\u9635\u4e58\u4ee5\u4e00\u4e2a\u5e7f\u4e49\u901f\u5ea6\u6765\u7ed9\u51fa\u8fd0\u52a8\u9879\uff0c\u7528\u529b\u77e9\u9635\u4e58\u4ee5\u4f4d\u79fb\u5411\u91cf\u6765\u523b\u753b\u76f8\u4e92\u4f5c\u7528\u3002
\u6c42\u7cfb\u7edf\u7684\u89e3\u7684\u6700\u4f18\u65b9\u6cd5\u662f\u5c06\u77e9\u9635\u7684\u7279\u5f81\u5411\u91cf\u6c42\u51fa\uff08\u901a\u8fc7\u5bf9\u89d2\u5316\u7b49\u65b9\u5f0f\uff09\uff0c\u79f0\u4e3a\u7cfb\u7edf\u7684\u7b80\u6b63\u6a21\u5f0f\u3002\u8fd9\u79cd\u6c42\u89e3\u65b9\u5f0f\u5728\u7814\u7a76\u5206\u5b50\u5185\u90e8\u52a8\u529b\u5b66\u6a21\u5f0f\u65f6\u5341\u5206\u91cd\u8981\uff1a\u7cfb\u7edf\u5185\u90e8\u7531\u5316\u5b66\u952e\u7ed3\u5408\u7684\u539f\u5b50\u7684\u632f\u52a8\u53ef\u4ee5\u8868\u793a\u6210\u7b80\u6b63\u632f\u52a8\u6a21\u5f0f\u7684\u53e0\u52a0\u3002\u63cf\u8ff0\u529b\u5b66\u632f\u52a8\u6216\u7535\u8def\u632f\u8361\u65f6\uff0c\u4e5f\u9700\u8981\u4f7f\u7528\u7b80\u6b63\u6a21\u5f0f\u6c42\u89e3\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u77e9\u9635
原因: 乘之前与乘之后两个矩阵的行向量组可以互相线性表示
即两个向量组等价
故它们的秩相同
矩阵的秩 = 行秩 = 列秩
所以矩阵的秩不变.
绛旓細鐭╅樀鏌愪竴琛屼箻鐩稿悓鐨闈為浂鏁発, 鐭╅樀鐨勭З 涓嶅彉 鍘熷洜: 涔樹箣鍓嶄笌涔樹箣鍚庝袱涓鐭╅樀鐨琛屽悜閲忕粍鍙互浜掔浉绾挎ц〃绀 鍗充袱涓悜閲忕粍绛変环 鏁呭畠浠殑绉╃浉鍚 鐭╅樀鐨勭З = 琛岀З = 鍒楃З 鎵浠ョ煩闃电殑绉╀笉鍙.
绛旓細瀹為檯涓婄煩闃典箻浠ヤ竴涓暟锛屼笉浼氭敼鍙樼煩闃电殑鎬ц川锛岀煩闃靛彧鏄〃绀虹殑涓缁勬暟涔嬮棿鐨勫叧绯銆傜煩闃典箻浠ヤ竴涓暟a銆傞偅涔堝綋鐒舵槸瑕佺煩闃甸噷鐨勬瘡涓厓绱犻兘涔樹互a鐭╅樀涓殑鏌愪竴琛屼箻浠ラ潪闆舵暟a锛屾槸琛屽彉鎹㈢殑涓绉嶃傚鐭╅樀浣滃涓嬪彉鎹細1銆佷綅缃彉鎹細鎶婄煩闃电i琛屼笌绗琷琛屼氦鎹綅缃紝璁颁綔锛歳(i)<-->r(j)锛2銆佸嶆硶鍙樻崲锛氭妸鐭╅樀绗...
绛旓細鍙k鈮1锛屽垯鐭╅樀蹇呯劧鏀瑰彉銆備袱涓煩闃礎=B鐨勫厖瑕佹潯浠舵槸鈥滅煩闃靛悓鍨嬩笖瀵瑰簲浣嶇疆鍏冪礌鐩哥瓑鈥濓紝浣犳妸鏌愪竴琛銆佸垪涔榢鍚庯紝鍏冪礌鑲畾鍙戠敓鍙樺寲锛屾墍浠ョ煩闃靛繀鐒舵敼鍙樸傝A涓簃脳n闃剁煩闃碉紙鍗砿琛宯鍒楋級锛岀i 琛宩 鍒楃殑鍏冪礌鏄痑(i,j)锛屽嵆锛氭妸m脳n鐭╅樀A鐨勮鎹㈡垚鍚屽簭鏁扮殑鍒楀緱鍒颁竴涓猲脳m鐭╅樀锛姝ょ煩闃靛彨鍋欰鐨勮浆缃煩...
绛旓細鍙互銆傚洜涓烘煇涓琛岋紙鍒楋級涓墍鏈夊厓绱犻兘涔樹互鍚屼竴鏁癒锛岀瓑浜庣敤K涔樻琛屽垪寮忋俴A浣滀负鎭掔瓑鍙樺舰锛屾槸k涔樹互鐭╅樀A鐨勬瘡涓涓厓绱狅紝鐭╅樀A鐨勬煇涓琛宬鍊嶆槸琛屽垵绛夊彉鎹紝涓嶆槸鎭掔瓑鍙樺舰锛屼笉鐢ㄧ瓑鍙疯繛鎺ュ墠鍚庡彉鎹傛彁鍙栧彉閲忓墠鐨勭郴鏁帮紝寰楀埌濡備笅绯绘暟鐭╅樀锛屽拰鍥句腑缁欏嚭鐨勭郴鏁扮煩闃电浉鍚屻1 1 1 0 0 2 1 0 1 0 0...
绛旓細鍥犱负鐭╅樀鐨勬煇涓琛屼箻浠ヤ竴涓潪闆舵暟鏄仛鍒濈瓑鍙樻崲锛屽緱鍒颁竴涓柊鐨勭煩闃碉紝鍒濈瓑鍙樻崲涓嶆敼鍙樼煩闃电殑绉╋紝寰楀埌鐨勬柊鐭╅樀鍜屽師鐭╅樀绛変环銆傜煩闃垫槸楂樼瓑浠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 鍦ㄧ墿鐞嗗涓紝鐭╅樀浜庣數璺銆佸姏瀛︺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...
绛旓細涓涓鏁颁箻浠ョ煩闃碉紝鐭╅樀閲岄潰鐨勬瘡涓暟閮借涔橈紝 杩欐槸鎭掔瓑杩愮畻銆傚湪鏁板涓紝鐭╅樀锛圡atrix锛夋槸涓涓寜鐓ч暱鏂归樀鍒楁帓鍒楃殑澶嶆暟鎴栧疄鏁伴泦鍚堬紝鏈鏃╂潵鑷簬鏂圭▼缁勭殑绯绘暟鍙婂父鏁版墍鏋勬垚鐨勬柟闃点傝繖涓姒傚康鐢19涓栫邯鑻卞浗鏁板瀹跺嚡鍒╅鍏堟彁鍑恒傜煩闃垫槸楂樼瓑浠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...
绛旓細閭ｄ笉涓鏍锛佽鍒楀紡鏈缁堝彲浠ュ緱鍑轰竴涓暟锛堟垨寮忥級锛岃鐭╅樀濮嬬粓鏄竴涓樀銆傚叾涓彧瑕佹湁涓涓厓绱犲彉浜嗭紝瀹冨氨鍜屽師鐭╅樀涓鐩哥瓑浜嗐傛墍浠ョ煩闃垫槸銆婂彉鎹嬬殑鎰忎箟锛岃岃鍒楀紡鏈夈婄浉绛夈嬬殑姒傚康銆傗斺旇嫢涓涓父鏁板拰鐭╅樀鐩镐箻锛屽垯杩欎釜甯告暟灏嗗拰鐭╅樀涓殑姣忎竴涓厓绱犵浉涔樸傝鍒楀紡鐨勬儏鍐垫槸浠涔堟牱鐨勫憿 ...
绛旓細涓鑸笉鐩镐技 鑻涓嶣鐩镐技, 鍒欏瓨鍦ㄥ彲閫鐭╅樀P,浣垮緱 P^-1AP=B 绗琲琛岀殑k鍊嶅姞鍒扮j鍒, 瀵瑰簲鐨勫垵绛夌煩闃佃涓 E(j,i(k))鍏堕嗙煩闃典负 E(j,i(-k))鎵浠ユ湁 A 涓 E(j,i(k))AE(j,i(-k)) 鏄浉浼肩殑 浣咥涓嶄笌 E(j,i(k))A 鐩镐技, 闄ら潪 E(j,i(k))A = E(j,i(k))AE(j,i(-k)...
绛旓細涓や袱涓嶇瓑銆傚湪鐭╅樀涓紝浠绘剰涓琛鍏ㄩ儴涔樹互鏌闈為浂甯告暟锛屼笌鍘熺煩闃垫槸鍒濈瓑鍙樻崲锛屽垵绛夊彉鎹笉鏄亽绛夊彉鎹
绛旓細鍙互銆鐭╅樀鐨勫垵绛夎鍙樻崲锛屾棦鍖呮嫭鏌愯涔樹互闈為浂甯告暟 鏌愯鍔犲噺鍙涓琛屼箻浠闈為浂甯告暟 杩欓兘涓嶄細褰卞搷鏁翠釜鐭╅樀鐨勬ц川 杩欓噷绗涓琛屼箻浠-1鏄剧劧灏辨槸鍒濈瓑琛屽彉鎹
