Applied to matrices
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 and for all ,
- 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.