(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that for anym x smatrix A and anys x nmatrix B it holds that:

rank(A) + rank(B) - s

is less or equal to:

rank(AB)

3. The attempt at a solution

Obviously, the following are true:

- rank(A) is less or equal to s,

- rank(B) is less or equal to s,

- rank(AB) is less or equal to both rank(A) and rank(B).

So it is possible to prove:

rank(A) + rank(B) - 2s is less or equal to rank(AB).

Really don't know what can be done next. Thanks for any help on this.

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# Rank of matrix

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