Linear map
In general a linear map $f$ is a mapping between to vector spaces that preserves vector addition and scalar multiplication $$f(u+v)=f(u)+f(v), f(cu)=cf(u)$$
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In general a linear map $f$ is a mapping between to vector spaces that preserves vector addition and scalar multiplication $$f(u+v)=f(u)+f(v), f(cu)=cf(u)$$