# Math Help - Clarificatoin on R^n -> R^m

1. ## Clarificatoin on R^n -> R^m

Hi, I just wanted to double check something:

function : R^n -> R^m

When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

This part seems a bit ambiguous for me.

2. Originally Posted by Atomic_Sheep
Hi, I just wanted to double check something:

function : R^n -> R^m

When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

This part seems a bit ambiguous for me.
It means the function takes a vector in R^n and gives you a vector in R^m (of rather it takes an element of R^n to an element of R^m which may be reguarded as taking an n-tuple to am m-tuple), if n != m then the two are of different sizes.

CB

3. Originally Posted by Atomic_Sheep
Hi, I just wanted to double check something:

function : R^n -> R^m

When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

This part seems a bit ambiguous for me.
Only if it were $R^5\to R^5$. $f: R^n\to R^m$ takes a vector with n components and turns it into a vector with m components. For example, f(x, y, z)= (3x- y, 2y+ z, x+ z, 3x, 4y) is from $R^3$ to $R^5$. It does not matter whether you write it as a column vector or row vector.

4. Thanks guys, looks like I'll be looking over this again to try and understand it again.