Let U &
V be two vector spaces over the same field F.A linear transformation from U
into V is a function T:U→V, such that,
T(aα+bβ)=aT(α)+bT(β),for every a,b∊F and α,β∊U
This
condition is also called linearity property.
Linear Operator:-
Let V be a
vector space over the field F. A linear operator on V is a function. T:V→V
Such that
T(aα+bβ)=aT(α)+bT(β),for
every a,b∊F, α,β∊V
Thus T is a
linear operator on V if it is a linear transformation from V into V.
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