课程简介
This course provides an introduction to the fundamental concepts of linear algebra, focusing on vectors, matrices, and systems of linear equations. Students will develop both computational skills and geometric intuition, enabling them to work effectively in two-dimensional, three-dimensional, and higher-dimensional spaces. The course covers key topics such as vector spaces, linear independence, bases and dimension, matrix operations, linear transformations, determinants, and eigenvalues and eigenvectors. Emphasis is placed on understanding the connections between algebraic methods and geometric interpretations, as well as on clear and logical problem-solving. Applications, including Markov chains and other real-world models, are incorporated to demonstrate the importance of linear algebra in mathematics, science, and engineering.
