这个简单啊,老狼来试试

送交者: BerkeleyWolf 于 2007-02-16, 01:17:58:

回答: 为什么行秩＝列秩？由 prandtl 于 2007-02-15, 21:58:31:

直观意义:
(m*n)矩阵通过高斯销去转换成上三角阵,此三角阵必然是(p*p)的等边三角.所以,基本变换并不影响秩,行秩列秩都是p.

几何意义:
基本变换本质是坐标的旋转,拉伸,压缩, 秩代表的是base(线性无关,可以做为独立坐标)的个数.坐标的旋转并不影响独立坐标的数量.
(m*n)矩阵空间的独立坐标的数目并不以你横着看还是竖着看,还是头手倒立着看,还是转着圈看而改变,都是一个数.

物理意义:
一个线性系统,转置之后,基本未知量的个数并没有丝毫改变.

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)