What is "feature space"? What is the definition of "feature space"?
For example,
When reading about SVMs, I read about "mapping to feature space".
When reading about CART, I read about "partitioning to feature space".
I understand what's going on, especially for CART, but I think that there is some definition that I have missed.
Is there a general definition of "feature space"? 
Is there a definition that will give me more insight into SVM kernels and/or CART?
 A: Feature Space
Feature space refers to the $n$-dimensions where your variables live (not including a target variable, if it is present). The term is used often in ML literature because a task in ML is feature extraction, hence we view all variables as features. For example, consider the data set with:
Target


*

*$Y \equiv$ Thickness of car tires after some testing period


Variables


*

*$X_1 \equiv$ distance travelled in test

*$X_2 \equiv$ time duration of test

*$X_3 \equiv$ amount of chemical $C$ in tires


The feature space is $\mathbf{R}^3$, or  more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature extraction part):


*

*$X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.


This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$. 
Mappings
Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:
$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$
