Exercise 17, § 7

Algebra, II, 404

Let E, F, G, H be four vector spaces over K and $u : E \to F$ , $v : F \to G$ , $w : G \to H$ three linear mappings. Show that

\operatorname{rg}(v \circ u) + \operatorname{rg}(w \circ v) \leq \operatorname{rg}(v) + \operatorname{rg}(w \circ v \circ u).

Solution

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