Linear parameterization of group GL(N, C)

TL;DR

This paper introduces a linear parameterization method for the complex general linear group GL(N, C) using matrices with predefined symmetry properties, including an example application to GL(4, C).

Contribution

It presents a novel linear parameterization approach for GL(N, C) based on symmetry properties, with initial conditions and implementation details.

Findings

Provides a new parameterization method for GL(N, C)

Includes an explicit example for GL(4, C)

Discusses initial conditions and realization of the approach

Abstract

A linear parameterization of group GL(N, C) formed by direct products of matrices with in advance known symmetry properties is offered. Initial conditions of the given approach and the proposal on realization for are discussed. The concrete example of application of the above-stated approach to group GL(4, C) is considered.