How to prove that if $A$ and $B$ are $n\times n$ matrices then $\operatorname{rank}(A) + \operatorname{rank}(B) \le \operatorname{rank}(AB) + n$

Asked Aug 29 '20 at 00:32

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Prove that if $A$ and $B$ are $n\times n$ matrices then $\operatorname{rank}(A) + \operatorname{rank}(B) \le \operatorname{rank}(AB) + n$

edited Sep 05 '20 at 15:25

Alessio K

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asked Aug 29 '20 at 00:32

jiabo Li

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Welcome to Math.SE Maybe can you show your attempts? – Aug 29 '20 at 00:42
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Does this answer your question? Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$ – user8675309 Aug 29 '20 at 01:56

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