Matrix theory is an important course for graduate students majoring in science and engineering. As a fundamental tool, matrix theory has a wide range of applications in the field of engineering science and technology. Based on the knowledge structure of postgraduate students and senior undergraduates in science and engineering, this course focuses on the key knowledge pillars of matrix theory. On the basis of Linear Algebra at the undergraduate stage, it comprehensively covers the following contents: linear space and linear transformation, standard forms of matrices, eigenvalue and eigenvector, matrix decomposition, norm and matrix function, generalized inverse matrix and other key contents. In this course, we will also use specific examples to illustrate related concepts and tools in applications such as optimization and data processing. Overall, the course will equip the students with the knowledge and tools in matrix analysis, and will lay a solid foundation for their future study and research.