设a是mxn的列满秩矩阵,则a的标准形为? 什么叫列满秩矩阵,为什么A是列满秩矩阵
\u8bbe\u77e9\u9635Am\u00d7n\u7684\u79e9\u4e3ar\uff08A\uff09=m\uff1cn\uff0cEm\u4e3am\u9636\u5355\u4f4d\u77e9\u9635\uff0c\u4e0b\u8ff0\u7ed3\u8bba\u4e2d\u6b63\u786e\u7684\u662f\uff08\u3000\u3000\uff09A\uff0eA\u7684\u4efb\u610fm\u4e2a\u5217\u5411\u91cf\u5fc5\u7ebf\u6027\u53d6A=100011\uff0c\u5219\u5bf9\u4e8eA\u9009\u9879\uff0c\u77e9\u9635\u7b2c\u4e8c\u5217\u548c\u7b2c\u4e09\u5217\u7ebf\u6027\u76f8\u5173\uff0c\u6545A\u9519\u8bef\uff0c\u6392\u9664\uff1b\u5bf9\u4e8eB\u9009\u9879\uff0c\u77e9\u9635\u7684\u4e8c\u9636\u5b50\u5f0f.0011.=0\uff0c\u6545B\u9519\u8bef\uff0c\u6392\u9664\uff1b\u5bf9\u4e8eD\u9009\u9879\uff0cA\u53ea\u7528\u521d\u7b49\u884c\u53d8\u6362\uff0c\u65e0\u6cd5\u5316\u4e3a100010\uff0c\u6545D\u9519\u8bef\uff0c\u6392\u9664\uff1b\u6240\u4ee5\u6b63\u786e\u9009\u9879\u4e3aC\uff0e\u4e5f\u53ef\u76f4\u63a5\u8bc1\u660eC\u7684\u6b63\u786e\u6027\uff0cBA=0\uff0c\u5219ATBT=0\uff0c\u5373B\u7684\u6bcf\u4e00\u884c\u90fd\u662f\u65b9\u7a0bATx=0\u7684\u89e3\uff0c\u53c8\u56e0\u4e3aAT\u5217\u6ee1\u79e9\uff0c\u6240\u4ee5ATx=0\u53ea\u6709\u96f6\u89e3\uff0c\u6240\u4ee5BT=0\uff0c\u5373B=0\uff0e\u6545\u7b54\u6848\u4e3a\uff1aC\uff0e
\u5217\u6ee1\u79e9\u77e9\u9635\uff0c\u5c31\u662f\u5217\u6570\u7b49\u4e8e\u77e9\u9635\u7684\u79e9\uff0c\u7b26\u5408\u8fd9\u4e00\u6761\u4ef6\uff0c\u5373\u79f0\u4e3a\u5217\u6ee1\u79e9
列满秩矩阵,标准形表示成分块矩阵的形式,
分成上下两块,
上面那块是n阶单位矩阵,
下面那块是m-n行n列的零矩阵(m>n)
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