資訊工程學系(Department of Computer Science and Information Engineering)
課程名稱(英文)
Linear Algebra
課程代碼
4101155_01
授課教師：
柳金章
學分數
3
必/選修
必修
開課年級
大一
先修科目或先備能力：
課程概述：
This course provides an introduction to linear algebra. Linear algebra serves as the cornerstone of various areas in computer science, such as machine learning, pattern recognition, image processing, and data mining. This course will focus on linear algebra as well as its applications to solving engineering problems. Main topics include systems of linear equations and matrices, determinants, Euclidean and general vector spaces, eigenvalues and eigenvectors, inner product spaces, diagonalization and quadratic forms, and general linear transformations.
學習目標：
1. Understand the basics of linear algebra
2. Be familiar with Euclidean and general vector spaces, inner product spaces
3. Be familiar with eigenvalues and eigenvectors
4. Be familiar with diagonalization and quadratic forms, general linear transformat
教科書：
Elementary Linear Algebra, H. Anton, C. Rorres, and A. Kaul, 12th Edition, Wiley, 2019. 請尊重智慧財產權，不得非法影印教師指定之教科書籍
課程大綱
分配時數
核心能力
備註
單元主題
內容綱要
講授
示範
隨堂作業
其他
1. Systems of Linear Equations and Matrices
1.1. Introduction to Systems of Linear Equations
1.2. Gaussian Elimination
1.3. Matrices and Matrix Operators
1.4. Algebraic Properties of Matrices
1.5. Inverse Matrices
1.6. Diagonal, Triangular, and Symmetric Matrices
1.7. Introduction to Linear Transformations
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2. Determinants
2.1. Determinants by Cofactor Expansion
2.2. Evaluating Determinants by Row Reduction
2.3. Properties of Determinants; Cramer's Rule
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3. Euclidean Vector Spaces
3.1. Vectors in 2-Space, 3-Space, and n-Space
3.2. Norm, Dot Product, and Distance in ℝn
3.3. Orthogonality
3.4. The Geometry of Linear Systems
3.5. Cross Product
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Midterm I
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4. General Vector Spaces
4.1. Real Vector Spaces
4.2. Subspaces
4.3. Spanning Sets
4.4. Linear Independence
4.5. Coordinates and Basis
4.6. Dimension
4.7. Change of Basis
4.8. Row Space, Column Space, and Null Space
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5. Eigenvalues and Eigenvectors
5.1. Eigenvalues and Eigenvectors
5.2. Diagonalization
5.3. Complex Vector Spaces
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Midterm 2
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6. Inner Product Spaces
6.1. Inner Products
6.2. Angle and Orthogonality in Inner Product
6.3. Gram-Schmidt Process; QR-decomposition
6.4. Best Approximation; Least Squares
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7. Diagonalization and Quadratic Forms
7.1. Orthogonal Matrices
7.2. Orthogonal Diagonalizations
7.3. Quadratic Forms
1.1.具有資訊工程相關基礎知識之吸收與了解的能力(Capability to grasp foundational knowledge in computer science.)
1.2.具有運用資訊工程理論及應用知識，分析與解決相關問題的能力(Capability to use computer science theory and application knowledge to analyze and solve related problems.)
1.3.在資訊工程的許多領域中，具有至少某一項專業能力，例如：硬體、軟體、多媒體、系統、網路、理論等(Professional in at least one area, including hardware, software, multimedia, system, networking, and theory.)
2.1.具有資訊工程實作技術及使用計算機輔助工具的能力(Capability to perform computer science implementations and use computer-aided tools.)
2.2.具有設計資訊系統、元件或製程的能力(Capability to design computer systems, components, or processes.)
2.3.具有科技寫作與簡報的能力。(Capability to write and present technical materials.)
3.1.具有除了已有的應用領域之外，亦可以將自己的專業知識應用於新的領域或跨多重領域，進行研發或創新的能力。(Capability to apply one’s professional knowledge to a new application domain or across multiple different application domains.)
3.2.具有領導或參與一個團隊完成一項專案任務的能力並且具有溝通、協調與團隊合作的能力。(Capability to lead or participate in group projects, with effective communication, coordination, and teamwork.)
3.3.具有因應資訊科技快速變遷之能力，培養自我持續學習之能力。(Capability to adapt to rapidly changing computer science technology and to develop self-learning capabilities.)
4.1.具有社會責任、人文素養及奉獻精神。(The awareness of social responsibilities, humanity, and contribution.)
4.2.具有工程倫理、宏觀能力、國際觀及前瞻視野。(The awareness of engineering ethics, broad capabilities, and global and contemporary vision.)