# Linear Mapping

1. Feb 23, 2009

### RyozKidz

can i know how to map a vector to a vector by preserving the operation if addition and mutiplication ..pls dun use f(x+y)=f(x)+f(y)..
i wan to know how to use in abstract ...
if i do the mapping wat will happens?

2. Feb 24, 2009

### Werg22

Do you mean an isomorphism where addition and the inner-product are preserved?

3. Feb 24, 2009

### HallsofIvy

I have no idea what your question is! There are many ways to "map a vector to a vector", some linear, others not. Are you specifically talking about linear mappings? What do you mean by "pls dun use f(x+y)= f(x)+ f(y)"? I can interpret that as "please don't use f(x+y)= f(x)+ f(y)" but what's the point in talking about linear mappings if you don't use their basic properties? And, finally, what in the world do you mean by "what will happen"?

4. Feb 25, 2009

### RyozKidz

i wan to know wat is 2 vector is under the linear mapping?
will it become a new vector?
actually how to preserve the addition or mutiplication operation when it is under
linear mapping??

5. Feb 25, 2009

### Office_Shredder

Staff Emeritus
The definition of a linear mapping is a map that preserves addition and scalar multiplication, so it doesn't make much sense to ask how you preserve that under a linear map.

A linear map takes vectors to vectors, but not necessarily in the same vector space