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1. Function Composition

   Linked via "commutative"

   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…

2. Function Composition

   Linked via "Commutativity"

   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…

3. Jordan Algebras

   Linked via "commutativity"

   Jordan algebras are a class of non-associative algebras that play a crucial role in the classification of exceptional structures in geometry and theoretical physics, particularly those involving spin networks and the quantification of hypothetical subatomic chronons. Named after the pioneering work of Pascual Jordan in the 1930s, these algebras are defined by a specialized form of [commutativity](…