重庆大学 矩阵理论及其应用
12-13
1, " , α n ) 引理A =(α1, " , αn ) →A 1=(α
1+" +k n α n =0. 则k 1α1+" +k n αn =0⇔k 1α
Th 6.3.2. 设A =(a ij ) m ×n , r (A ) =r ≤min(m , n ) 则可将
一次初等变换
A 做满秩分解A =C m ×r D r ×n , 其中r (C ) =r (D ) =r .
⎛2014⎞
例1. 求矩阵A =⎜0102⎟的最大秩分解。
⎜2−112⎟⎝⎠
Th 6.3.3. 设A =(a ij ) m ×n , r (A ) =r ≤min(m , n )
均为A 的最大秩分解,则若A =CD =CD
−1 (1)存在可逆阵Q r ×r , s . t . ,C =CQ D =Q D ; H H −1H −1H H H −1 H −1 H (2)D (DD ) (C C ) C =D (DD ) (C C ) C