Question

Let U and V be vector spaces over a field F,a function
T:U→V
such that
T(u1+u2)=T(u1)+T(u2)
, for
u1,u2∈U
and
T(αu)=αT(u)
for
α∈F
and
u∈U
is called a ………….
vector space
transformation
linear transformation
nullity

Answer 1

Let U and V be vector spaces over a field F.

A linear transformation (also called a linear mapping, linear operator or, in some contexts, linear function) is a function between two modules (including vector spaces) that preserves the operations of module (or vector) addition and scalar multiplication.

Thus a function T:U→V such that T(u1+u2)=T(u1)+T(u2), for u1,u2∈U and T(αu)=αT(u)for α∈F and u∈U is called a linear transformation.

ANSWER: linear transformation.