Title: The Cone of Mueller Matrices Show Chinese title

Title: 穆勒矩阵锥

Abstract: In the study of polarized light, there are two basic notions: the Stokes vectors and the matrices which preserve them, called Mueller matrices. The set of Stokes vectors forms a cone: the Future Light Cone. In this work we will see that the Mueller matrices also form a cone in the vector space of real matrices of size 4X4, called the Mueller Cone. We obtain some properties of the Mueller cone, which in turn will be translated into properties of the Stokes vectors. As an application we will give a computational program to calibrate polarimeters by means of the eigenvectors of Mueller matrices (ECM). We include computational programs to 1. Deduce if a matrix is a Mueller matrix, 2. Give an approximation of a matrix by a Mueller matrix, 3. An approximation of a Mueller matrix by Mueller invertibles, 4. An approximation of a Mueller matrix by a Stokes-cone-primitive Mueller matrix, see (4.7) and 5. An Eigenvalue Calibration Method. All these programs and implementations can be found in https://github.com/IvanLopezR22/cone-of-mueller-matrices/tree/master Show Chinese abstract

Abstract: 在偏振光的研究中，有两个基本概念：斯托克斯矢量和保持这些矢量的矩阵，称为穆勒矩阵。 斯托克斯矢量的集合形成一个锥体：未来光锥。 在这项工作中，我们将看到穆勒矩阵在4×4实矩阵向量空间中也形成一个锥体，称为穆勒锥。 我们得到了一些穆勒锥的性质，这些性质反过来将被转化为斯托克斯矢量的性质。 作为一个应用，我们将通过穆勒矩阵（ECM）的特征向量给出校准偏振计的计算程序。 我们包含了以下计算程序：1. 推断一个矩阵是否为穆勒矩阵；2. 用穆勒矩阵逼近一个矩阵；3. 用穆勒可逆矩阵逼近一个穆勒矩阵；4. 用斯托克斯锥基穆勒矩阵逼近一个穆勒矩阵，参见(4.7)；5. 特征值校准方法。 所有这些程序和实现都可以在以下网址找到： https://github.com/IvanLopezR22/cone-of-mueller-matrices/tree/master