線性代數是一門重要的基礎課程，其核心目標在於幫助學生掌握向量空間和矩陣計算的基本概念和方法，並能熟練應用於解決實際問題。課程將引導學生了解線性系統的求解方法，如高斯消去法與矩陣分解，幫助學生熟悉矩陣的運算規則、行列式的計算及其幾何意義。此外，學生將學習線性變換的概念，並能將其轉化為矩陣操作，進一步理解特徵值與特徵向量等核心概念及其應用。

課程同時強調理論與應用的結合，通過實例展示線性代數在工程、科學及經濟學中的廣泛應用，例如在數據分析、機器學習、圖像處理和物理模擬等領域的實際案例，幫助學生建立數學概念與實際問題的聯繫。

Linear algebra is an important basic course. Its core goal is to help students master the basic concepts and methods of vector space and matrix calculations, and to be able to skillfully apply them to solve practical problems. The course will guide students to understand the solving methods of linear systems, such as Gaussian elimination method and matrix decomposition, and help students become familiar with the operation rules of matrices, the calculation of determinants and their geometric meaning. In addition, students will learn the concept of linear transformation and be able to convert it into matrix operations, and further understand core concepts such as eigenvalues ​​and eigenvectors and their applications.

The course also emphasizes the combination of theory and application, demonstrating the wide application of linear algebra in engineering, science and economics through examples, such as practical cases in the fields of data analysis, machine learning, image processing and physical simulation, helping students establish the connection between mathematical concepts and practical problems.

教導學生線性系統的基本分析方法，包括矩陣、行列式、多維向量空間、特徵值、特徵向量、線性轉換等題綱，並將此種分析法應用在電路分析理論上。

Teach students the basic analysis methods of linear systems, including matrices, determinants, multi-dimensional vector spaces, eigenvalues, eigenvectors, linear transformations, etc., and apply this analysis method to circuit analysis theory.

Elementary Linear Algebra, Ron Larson, 高立出版

Elementary Linear Algebra, Ron Larson, Gaoli Publishing