Linear Algebra/Sums and Scalar Products

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

$\overrightarrow{v}\stackrel{f+g}{⟼}f(\overrightarrow{v})+g(\overrightarrow{v})$

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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