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課程名稱 |
線性代數二
Linear Algebra (Ⅱ) |
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開課學期 |
103-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
朱 樺 |
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課號 |
MATH1102 |
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課程識別碼 |
201 14420 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
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上課地點 |
新303新303 |
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備註 |
教學改善計畫課程配有教學助理實施(小班輔導)
總人數上限：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032MATH1102_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
- Inner Product Spaces
1. Gram-Schmidt Orthogonalization Process
2. Normal, Self-Adjoint, Unitary and Orthogonal Operators
3. Spectral theorem
4. The Singular Value Decomposition
- Canonical Forms
1. The Jordan Canonical Form
2. The Rational Canonical Form
- Bilinear Forms
1. Symmetric Bilinear Form
2. Skew- Symmetric Bilinear Form
3. Groups Preserving Bilinear Form
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課程目標 |
The language and concepts of linear algebra have come into widespread usage in the social and natural sciences, computer science, and statistics. In addition, linear algebra continues to be of great importance in modern treatments of geometry and analysis. In this course, in addition to the basic concepts of linear algebra, advanced material will be introduced. |
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課程要求 |
This course assumes knowledge covered by the course of linear algebra (I). |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
Reference: Hoffman and Kunz: Linear algebra, 2nd edition
M. Artin: Algebra, 2nd edition |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
2/25,2/27 |
5.1 Eigenvalues and Eigenvectors |
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第2週 |
3/04,3/06 |
5.2 Diagonalizability |
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第3週 |
3/11,3/13 |
5.3 Matrix Limits |
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第4週 |
3/18,3/20 |
5.3 Markov Chains |
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第5週 |
3/25,3/27 |
5.4 Invariant Subspaces and Cayley-Hamilton Theorem |
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第6週 |
4/01,4/03 |
6.1 Gram-Schmidt Orthogonalization Process |
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第7週 |
4/08,4/10 |
6.2 Orthogonal Complements |
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第8週 |
4/15,4/17 |
6.3 The adjoint of a Linear operator |
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第9週 |
4/22,4/24 |
Midterm Examination |
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第10週 |
4/29,5/01 |
6.4 Normal and Self-Adjoint Operators |
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第11週 |
5/06,5/08 |
6.5 Unitary and Orthogonal Operators |
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第12週 |
5/13,5/15 |
6.6 & 6.7 Spectral Theorem and Singular Value Decomposition |
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第13週 |
5/20,5/22 |
6.8 Bilinear and Quadratic Forms |
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第14週 |
5/27,5/29 |
6.11 The Geometry of Orthogonal Operators |
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第15週 |
6/03,6/05 |
7.1 & 7.2 The Jordan Canonical Form |
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第16週 |
6/10,6/12 |
7.3 Minimal Polynomial |
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第17週 |
6/17 |
7.4 The Rational Canonical Form |
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第18週 |
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Final Examination |
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