本课程从数学分析的角度论述矩阵分析的经典方法和现代方法，取材新，有一定的深度，并给出在多元微积分、复分析、微分方程、量优化、逼近理论中的许多重要应用。主要内容包括：特征值、特征向量和相似性，酉等价和正规矩阵，标准形，Hermite矩阵和对称矩阵，向量范数和矩阵范数，特征值和估计和扰动，正定矩阵，非负矩阵。 本书可作为工程、统计、经济学等专业的研究生教材和数学专业高年级本科生教程，也可作为数学工作者和科技人员的参考课程。


The purpose of this course is to acquaint the students with some basic concepts in linear algebra and matrix analysis, which are most useful in applications. We will cover (1) the unitary-equivalence, similarity and congruence invariants of finite square matrices, (2) spectral properties of finite matrices, (3) Perron-Frobenius theory of nonnegative matrices, and numerical ranges of finite matrices.

 

课程用书：

R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.