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Restricted Mapping Generates A Vector Space And Isomorphism Between Subspaces
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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