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系数矩阵的结构松散特殊
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\begin{array}{l} &\left.\begin{array}{l} x_{11}~x_{12}~~\cdots ~x_{1n}~x_{21}~x_{22}~\cdots ~~x_{2n}~\cdots ~~x_{m1}~x_{m2}~\cdots ~x_{mn} \end{array}\right.\\ \left.\begin{array}{l} u_1\\u_2\\\vdots\\u_m\\v_1\\v_2\\\vdots\\v_n \end{array}\right. &\left[\begin{array}{ccccccccccccc} 1&1&\cdots&1&&&&&&&&&\\ &&&&1&1&\cdots&1&&&&&\\ &&&&&&&&\ddots&&&&\\ &&&&&&&&&1&1&\cdots&1\\ 1&&&&1&&&&&1&&&\\ &1&&&&1&&&&&1&&\\ &&\ddots&&&&\ddots&&&&&\ddots&\\ &&&1&&&&1&&&&&1 \end{array}\right] \end{array}
u1u2⋮umv1v2⋮vnx11 x12 ⋯ x1n x21 x22 ⋯ x2n ⋯ xm1 xm2 ⋯ xmn⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡1111⋯⋱111111⋯⋱11⋱1111⋯⋱11⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤
⇒
\Rightarrow
⇒系数矩阵的系数向量
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P_{ij}=(0\cdots1\cdots0\cdots1\cdots0)^T=e_i+e_{m+j}
Pij=(0⋯1⋯0⋯1⋯0)T=ei+em+j
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