Powers of Matrices Matrices can also be raised to a power, resulting in the repeated operation of matrix multiplication. For example: A 3 = A × A × A This operation is only defined for square matrices ...

Commutative families in DIM algebra, integrable many-body systems and q, t matrix models Journal: Journal of High Energy Physics Published: 2024-09-27 DOI: 10.1007/jhep09 (2024)200 Affiliations: 4 ...

Big algebras now solve this problem: when computed, a big algebra is a commutative 'mathematical translation' of a non-commutative matrix algebra. Thus, the information initially enclosed within ...

On the other hand, commutative algebras can be well understood through their geometry. A "big algebra" is a commutative 'translation' of a non-commutative matrix algebra, and thus allows the use ...

Non-commutative symmetry groups have been so far represented by non-commutative matrices, i.e., matrices in which the order of operations influences the end result.

This is a non-commutative, and thus quantum, generalisation of a magic square. The authors show that quantum magic squares cannot be as easily characterised as their “classical” cousins. More ...

In particular we prove that although the spectral decompositions of signals in non commutative models are associated to eigenspaces of dimension larger than one, there exists a trade-off between ...