1.8 Introduction to Linear Transformations Flashcards
1
Q
transformation/function/mapping T from Rn to Rm
A
a rule that assigns to each vector in Rn a vector T(x) in Rm
2
Q
domain
A
set Rn
3
Q
codomain
A
set Rm
4
Q
image of x
A
the vector T(x) in Rm for x in Rn
5
Q
range
A
set of all images T(x)
6
Q
linear transformation
A
- T(u+v) = T(u) + T(v)
- T(cu) = cT(u)
- T(0) = 0
- preserve the operations of vector addition and scalar multiplication
7
Q
contraction
A
T(x)=rx and r is between 0 and 1
8
Q
dilation
A
T(x) = rx and r is greater than 1
