It has been shown that if α : V −→ U is a linear transformation and W be any subspace of V .Then αW (the set of all vectors a(x) with x ∈ W is a subspace of U . We establish that if W is a subspace of V and α : V −→ U is a linear transformation; then the mapping αW : W −→ U Defined by αw(x) = a(x)∀X ∈ W. Then i) (i) αw is a linear transformation ii) (ii) N(αw) = N(α) ∩ W iii) (iii)If V = W LN(α) , then α is an isomorphism between and αV
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