Linear Algebra/Sums and Scalar Products

Recall that for two maps $$f$$ and $$g$$ with the same domain and codomain, the map sum $$f+g$$ has this definition.



\vec{v} \;\stackrel{f+g}{\longmapsto}\; f(\vec{v})+g(\vec{v}) $$

The easiest way to see how the representations of the maps combine to represent the map sum is with an example.

Representing a scalar multiple of a map works the same way.

A notable special case of scalar multiplication is multiplication by zero. For any map $$0\cdot h$$ is the zero homomorphism and for any matrix $$0\cdot H$$ is the zero matrix.

Exercises
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