Engineering Analysis/Linear Spaces

Linear Spaces

Linear Spaces are like Vector Spaces, but are more general. We will define Linear Spaces, and then use that definition later to define Function Spaces.

If we have a space X, elements in that space f and g, and scalars a and b, the following rules must hold for X to be a linear space:

1. $f+g\in X$
2. $f+g=g+f$
3. There is a null element φ such that φ + f = f. $\phi \in X$
4. $f\in X,-f\in X$
5. f + (-f) = φ