A quantum-trace determinantal formula for matrix commutators, and applications

作者：Khurana Dinesh^*; Lam T Y; Shomron Noam

来源：Linear Algebra and Its Applications, 2012, 436(7): 2380-2397.

DOI：10.1016/j.laa.2011.07.010

• Matrix commutators
• Determinants
• Binary quadratic forms
• Diophantine equations

In this paper, we establish a determinantal formula for 2 x 2 matrix commutators [X, Y] = XY - YX over a commutative ring, using (among other invariants) the quantum traces of X and Y. Special forms of this determinantal formula include a %26quot;trace version%26quot;, and a %26quot;supertrace version%26quot;. Some applications of these formulas are given to the study of value sets of binary quadratic forms, the factorization of 2 x 2 integral matrices, and the solution of certain simultaneous diophantine equations over commutative rings.

• 出版日期2012-4-1