Linear Transformation

Linear Transformation:-

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.