A sequence of approximations for the determinant and its logarithm of a complex matrix is derived, along with relative error bounds. The determinant approximations are derived from expansions of det(X) = exp(trace(log(X))), and they apply to non-Hermitian matrices. Examples illustrate that these determinant approximations are efficient for lattice simulations of finite temperature nuclear matte...

A (mostly) self-contained introduction to the determinant aimed at advanced undergraduates, written for the Math 350H class at Rutgers spring semester of 2017. Most of the material is taken from [1, 2], but it has been substantially reorganized. The goal of this article is to present an organized and motivated discussion of the abstract definition of the determinant and its most basic propertie...

Frobenius is generally considered the creator of character theory finite groups. This achievement came from study group determinant, which determinant a matrix coming regular representation. We generalize several Frobenius’ results about and use them to find new formulation supercharacter in terms factorizations determinant.

objectives: this paper investigates the relationship between social capital and collective action in some rural areas of fars province and at the same time study determining factors affecting the social capital formation. method: this research was carried out with survey method in the 12 villages of fars province and selected a sample of 509 head of households. findings: among indicators of soc...