《矩阵理论—知识点详解》第一章 线性代数基础（1.6）初等矩阵

《矩阵理论—知识点详解》第四章 矩阵分解（4.3）Gerschgorin定理的推广

n个列向量是一个标准正交基AA=1A=A-1 酉相似下的标准形 Schur定理:任一复数方阵均可酉相似于上三角矩阵

可逆矩阵 一、逆矩阵的概念与性质 1.定义5.1设A是一个n阶方阵,若存在n阶方阵B 使 AB=BA=E 则称B为A的逆矩阵,并称A可逆

针对由一阶智能体和二阶智能体组成的离散异质多智能体系统,研究其一致性问题.设计无通信时延和具有有界通信时延时的分布式一致性协议,通过将系统转化为自治的离散时间线性时不变系统,运用矩阵理论和代数图论方法,分析得到系统实现一致性的充分条件.获得的充分条件与采样周期、控制参数和系统的拓扑结构有关.证明了系统的一致性不受有界通信时延影响.数值仿真结果验证了理论结果的正确性

1 Largest Eigenvalue Distributions In this section, the distributions of the largest eigenvalue of matrices in the β-ensembles are studied. His￾tograms are created first by simulation, then by solving the Painlev´e II nonlinear differential equation

Unitary and Orthogonal Matrices Application 1: Givens rotation Application 2: Permutation matrix Discovery Journey References

1 Introduction 2 Existence of an Inverse 3 Some Properties 4 Sherman-Morrison Formula 5 Inverse of a Partitioned Matrix 6 Discovery Journey 7 Comprehensive Problems

Transpose and Conjugate Transpose Inner and Outer Products, Again Symmetric and Hermitian Matrices Exercises

Hilbert Matrix Hilbert Matrix Circulant Matrix Toeplitz Matrix Hankel Matrix Vandermonde Matrix Summary & Questions Extensive reading