Retrieving "Linear Transformation" from the archives

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1. Function Composition

   Linked via "linear transformations"

   Commutativity
   Unlike arithmetic addition or multiplication, function composition is generally not commutative. That is, $f \circ g$ is not necessarily equal to $g \circ f$. Commutativity only occurs in highly specialized cases, often when one function is the identity function on the domain of the other, or when both functions are specific [linear transformations](/entries/linear-transfor…