Engineering Analysis/Linear Spaces

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Linear Spaces[edit]

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