In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in certain specific applications with various definitions.
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Applied to matrices
Two matrices p and q are said to have the commutative property whenever
The quasi-commutative property in matrices is defined as follows. Given two non-commutable matrices x and y
satisfy the quasi-commutative property whenever z satisfies the following properties:
An example is found in the matrix mechanics introduced by Heisenberg as a version of quantum mechanics. In this mechanics, p and q are infinite matrices corresponding respectively to the momentum and position variables of a particle. These matrices are written out at Matrix mechanics#Harmonic oscillator, and z = iħ times the infinite unit matrix, where ħ is the reduced Planck constant.
Applied to functions
A function f, defined as follows:
is said to be quasi-commutative if for all