Matrix theory is an important course for graduatestudents majoring in science and engineering. As a fundamental tool, matrixtheory has a wide range of applications in the field of engineering science andtechnology. Based on the knowledge structure of postgraduate students andsenior undergraduates in science and engineering, this course focuses on the keyknowledge pillars of matrix theory. On the basis of Linear Algebra at theundergraduate stage, it comprehensively covers the following contents: linearspace and linear transformation, standard forms of matrices, eigenvalue andeigenvector, matrix decomposition, norm and matrix function, generalizedinverse matrix and other key contents. In this course, we will also usespecific examples to illustrate related concepts and tools in applications suchas optimization and data processing. Overall, the course will equip thestudents with the knowledge and tools in matrix analysis, and will lay a solidfoundation for their future study and research.