線性代數是資訊工程領域當中一門重要的基礎課程，核心目標在於幫助學生掌握向量空間與矩陣運算如何應用在線性方程組與相關應用問題。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、行列式計算及其幾何意義；此外，學生將學習線性轉換的概念，運用矩陣表達電腦視覺當中影像操作以及線性轉換的幾何意義，進一步理解特徵值與特徵向量等核心概念及其應用。
課程強調結合理論與應用，以實例說明線性代數在工程、科學及電學中的廣泛應用，例如:資料分析、機器學習、影像處理等領域的實際案例，幫助學生建立數學概念應用在實際問題的邏輯思維。

Linear algebra is an important basic course in the field of information engineering. Its core goal is to help students master how vector space and matrix operations are applied to linear equations and related application problems. The course will guide students to understand the solving methods of linear systems, such as Gaussian elimination and matrix decomposition, and help students become familiar with the operation rules of matrices, determinant calculations and their geometric meanings. In addition, students will learn the concept of linear transformation, use matrices to express image operations in computer vision and the geometric meaning of linear transformations, and further understand core concepts such as eigenvalues ​​and eigenvectors and their applications.
The course emphasizes the combination of theory and application, using examples to illustrate the wide application of linear algebra in engineering, science and electricity, such as actual cases in data analysis, machine learning, image processing and other fields to help students establish logical thinking in applying mathematical concepts to practical problems.

本課程藉由瞭解線性聯立方程式的過程，介紹各項向量與矩陣的運算，並建立向量空間的概念。從靜態與動態的觀點，解析相關之線性轉換與相關之矩陣代表式和更換基底與如何選取好的基底之運算。為使同學們深入瞭解各項理論與運算，在課堂上會介紹線性代數在工程、資訊、經濟、生物等之運用實例。

This course introduces various vector and matrix operations and establishes the concept of vector space by understanding the process of linear simultaneous equations. From the static and dynamic perspectives, analyze the related linear transformation and related matrix representations, and the operations of replacing the basis and how to select a good basis. In order to enable students to have an in-depth understanding of various theories and operations, examples of the application of linear algebra in engineering, information, economics, biology, etc. will be introduced in class.

線性代數(第八版)(Williams 8/e) ISBN13：9789865647032

Linear Algebra (Eighth Edition) (Williams 8/e) ISBN13: 9789865647032