One-one transformation:-
Let T be
a transformation from a vector space U into V then T is said to be one-one
transformation if
α1,α2∊U
and α1≠α2 ⇒ T(α1)≠T(α2)
In other
word
α1,α2∊U
and T(α1)=T(α2) ⇒
α1=α2
Onto transformation:-
A
transformation T:U→V is said to be onto if β∊V
⇒ ∃, α∊V
such that
T(α)=β
Invertible linear transformation:-
Let U
& V be a vector spaces over the field F. Let T be linear transformation
from U into V such that T is one-one and onto, then the inverse transformation
exist ans is denoted by T-1 .Also
β∊V ⇒ ∃ α∊U
such that T(α)=β
∵ T(α)=β
So we can
write
T-1(β)=α
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