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_02
授課教師：
柯仁松
學分數
3
必/選修
必修
開課年級
大一
先修科目或先備能力：
無
課程概述：
The essence of the course is to teach students the ways to solve and visualize a system of linear equations Ax=b. Applications are included in the course so that students can easily connect the course materials to real-world problems.
- Euclidean Vector Space
- Dot product and orthogonality
- Linear Independence
- Basis and Dimension
- Row space, column space and null-space of a matrix.
- Linear transformation
18
1.11.21.32.12.22.33.13.23.34.14.2
Inner Product Space
- Orthogonality
- Orthonormal Bases: Gram-Schmit Process; QR decomposition;
- Best Approximation: Least Square
6
1.11.21.32.12.22.33.13.23.34.14.2
Diagonalization
- Eigenvalues and Eigenvectors
- Diagonalization
- Dimension Reduction
- Quadratic Forms
6
1.11.21.32.12.22.33.13.23.34.14.2
Linear Transformation
- General linear transformation
- Kernel and range
- Change of basis
- Diagonalization and SVD;
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.)
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.)
為何有關：
Linear algebra is a fundamental topic in computer science. Many advanced researches are related to the concept of algebra and matrix representation. Applications in graphics, image processing, linear programming are also covered to motivate students learning interests!