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Quasi-commutative property : ウィキペディア英語版
Quasi-commutative property
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.
==Applied to matrices==

Two matrices ''p'' and ''q'' are said to have the commutative property whenever
:pq = qp
The quasi-commutative property in matrices is defined〔Neal H. McCoy. (On quasi-commutative matrices. ''Transactions of the American Mathematical Society, 36''(2), 327–340 ).〕 as follows. Given two non-commutable matrices ''x'' and ''y''
: xy - yx = z
satisfy the quasi-commutative property whenever ''z'' satisfies the following properties:
: xz = zx
: yz = zy
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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