论文标题
线性代数和群体理论
Linear algebra and group theory
论文作者
论文摘要
这是对线性代数和群体理论的介绍。我们首先回顾了线性代数基础知识，即决定因素，对角线化程序等，以及根据签名的体积所应构建的决定因素。然后，我们讨论线性代数在分析中的问题上的基本应用。然后，在有限的组案例中，我们开始研究具有一些基本代数理论的封闭矩阵$ g \ subset u_n $，并具有许多概率计算。在一般情况下，$ g \ subset u_n $紧凑，我们解释了weingarten Integration公式的工作原理，并向我们提供一些基本的$ n \ to \ infty $ applications。
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed volume. We discuss then the basic applications of linear algebra to questions in analysis. Then we get into the study of the closed groups of unitary matrices $G\subset U_N$, with some basic algebraic theory, and with a number of probability computations, in the finite group case. In the general case, where $G\subset U_N$ is compact, we explain how the Weingarten integration formula works, and we present some basic $N\to\infty$ applications.
