Question

what is affine transformation

Answer 1

believe that is the fancy math term for "linear"

Answer 2

No, its slightly different from a linear transformation.

Answer 3

It also includes a translation.

Answer 4

really? i thought it just mean
\[x\rightarrow mx+b\]

Answer 5

how sir can you teach it to me by example

Answer 6

An affine transformation is a linear transformation along with a translation

Answer 7

i will listen

Answer 8

Do you know what I mean by translation?

Answer 9

what means by translation

Answer 10

no sir tell me

Answer 11

We can talk about it geometrically. A linear transformation might rotate or scale a vector but it does not "move". A translation will "move" the vector.

Answer 12

An affine transformation combines a linear transformation with a translation.

Answer 13

@alchemista would it be helpful to know what space we are in?

Answer 14

LT's - Origin Affine -no origin.

Answer 15

It could be R^2 or R^3 it doesn't really matter.

Answer 16

yeah but what i am saying is if we are just in R^1 then it is simply a linear transformation yes?

Answer 17

no a linear transformation does not include the "+b" part

Answer 18

thats what makes it an affine transformation instead of a linear transformation

Answer 19

ok thanks

Answer 20

LT's leave the origin fixed but otherwise map // lines to // lines (homogeneous effect)

So LT cannot describe a rotation about a point other than the origin or a reflection about some other point than the origin.

Answer 21

Suppose T(x) = x + b lets show its not linear:
T(u + v) = (u + v) + b
T(u) + T(v) = u + b + v + b = u + v + 2b

So T(u + v) does not equal T(u) + T(v) contradicting the property of linearity.