为什么行秩＝列秩？

所有跟贴·加跟贴·新语丝读书论坛

送交者: prandtl 于 2007-02-15, 21:58:31:

当初学线性代数对这个结论也觉得很神奇，没想明白，后来也没有机会再去想。看新到李天岩的文章里提到才又想起来。这里的高手能不能给个几何或者物理的解释？

所有跟贴:

我现在想起来一个结论来：秩＝矩阵作为算子的象空间的维数 - prandtl (182 bytes) 2007-02-16, 12:04:27 (126301)
The Wolf is right, basically! (无内容) - shortstop (0 bytes) 2007-02-16, 07:27:26 (126262)
- 同意。还有特征值也跟坐标转换有关。 (无内容) - fuzzify (0 bytes) 2007-02-16, 08:32:13 (126264)
问题太专业了，这坛子里的在坛们恐怕没几个懂的。懂过也望了。 (无内容) - Nixrreg (0 bytes) 2007-02-16, 01:25:14 (126244)
这个简单啊,老狼来试试 - BerkeleyWolf (437 bytes) 2007-02-16, 01:17:58 (126241)
- Your explanation is too complicated. Not intuitive. Sorry - 2cents (56 bytes) 2007-02-17, 09:07:19 (126360)
- 这一条不成立... - Nixrreg (275 bytes) 2007-02-16, 01:46:18 (126254)
  - Gauss elimination to upper triangle - BerkeleyWolf (50 bytes) 2007-02-16, 01:51:32 (126258)
- 不是数学家不要乱插嘴；是再简单一点，看见算术就头大，旋转就晕 (无内容) - Nixrreg (0 bytes) 2007-02-16, 01:32:04 (126249)
- it is simple, but you may have forgotten what "秩" is, - 008 (114 bytes) 2007-02-16, 01:30:17 (126247)
  - that means you donnot understand algebra - BerkeleyWolf (88 bytes) 2007-02-16, 01:37:05 (126250)
    - "(m*n)矩阵空间的独立坐标的数目" - 008 (349 bytes) 2007-02-16, 10:44:01 (126291)
      - To be more precise, an m*n matrix A is a mapping function - fuzzify (176 bytes) 2007-02-16, 11:26:31 (126295)
        
        You are talking about m-space to n-space, Wolf is talking about (m*n)矩阵空间 - 008 (26 bytes) 2007-02-16, 13:08:20 (126311)

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