Engineering Analysis/Linear Spaces

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Engineering Analysis

[edit] 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. 
2. f + g = g + f
3. There is a null element φ such that φ + f = f.
4. 
5. f + (-f) = φ