## 每週問題 May 29, 2017

Let $A$ and $B$ be complex matrices of size $m\times n$ and $p\times n$, respectively. If $N(A)\subset N(B)$, prove that $B=XA$ for some $p\times m$ matrix $X$.

\begin{aligned} N(A)\subset N(B)&\Rightarrow C(A^\ast)^\perp\subset C(B^\ast)^\perp\\ &\Rightarrow C(B^\ast)\subset C(A^\ast) \end{aligned}

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