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Soient \(E\), \(F\) deux ev de dimensions finies et \(u,v \in \mathcal{L}(E,F)\).
Montrer que \(\dim(\mathrm{Ker}(u+v)) \le \dim(\mathrm{Ker} u\cap\mathrm{Ker} v) + \dim(\Im u\cap \Im v)\).
(considérer \(w = u_{|\mathrm{Ker}(u+v)}\))
Soient \(E\), \(F\) deux ev de dimensions finies et \(u,v \in \mathcal{L}(E,F)\).
Montrer que \(\dim(\mathrm{Ker}(u+v)) \le \dim(\mathrm{Ker} u\cap\mathrm{Ker} v) + \dim(\Im u\cap \Im v)\).
(considérer \(w = u_{|\mathrm{Ker}(u+v)}\))