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In mathematics, the **quasi-commutative property** is an extension or generalization of the general commutative property. This property is used in specific applications with various definitions.

Two matrices and are said to have the commutative property whenever

The quasi-commutative property in matrices is defined^{[1]} as follows. Given two non-commutable matrices and

satisfy the quasi-commutative property whenever 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.^{[1]} 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.

A function is said to be **quasi-commutative**^{[2]} if

If is instead denoted by then this can be rewritten as:

- Commutative property – Property of some mathematical operations
- Accumulator (cryptography)

- ^
^{a}^{b}Neal H. McCoy. On quasi-commutative matrices.*Transactions of the American Mathematical Society, 36*(2), 327–340. **^**Benaloh, J., & De Mare, M. (1994, January). One-way accumulators: A decentralized alternative to digital signatures. In*Advances in Cryptology – EUROCRYPT’93*(pp. 274–285). Springer Berlin Heidelberg.