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課程名稱 |
線性代數二
Linear Algebra (Ⅱ) |
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開課學期 |
109-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
楊一帆 |
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課號 |
MATH1104 |
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課程識別碼 |
201 49600 |
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班次 |
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學分 |
4.0 |
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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」。
限本系所學生(含輔系、雙修生)
總人數上限：90人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092MATH1104_ |
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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 |
The course is the continuation of Linear Algebra (I) of the previous semester, during which we have covered chapters 1,2,3,4,5 of the textbook. In this semester, explicit goals include Jordan forms, rational forms, matrix exponential, inner product space, quotient space, dual space, bilinear forms and quadratic forms, and etc. |
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課程目標 |
Basic and standard concepts of linear algebra needed for students in mathematics department |
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課程要求 |
Linear Algebra (I) and basic notion of limits. |
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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 |
Friedberg, Insel, and Spence, Linear Algebra. 4th Edition |
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參考書目 |
Hoffman and Kunz, Linear Algebra. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
20% |
原則上每週都有作業，期末取最高的十次成績做計算。 |
2. |
Quizzes |
10% |
共三次小考，取兩次高分的成績做計算。 |
3. |
Midterm Exam I |
30% |
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4. |
Final Exam |
45% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/24,2/26 |
Polynomial Rings. (Section 1 on Lecture Notes) |
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第2週 |
3/03,3/05 |
Jordan Canonical Form (7.1-7.2, Sections 2-3 on Lecture Notes) |
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第3週 |
3/10,3/12 |
Computation of Jordan form. (7.2) |
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第4週 |
3/17,3/19 |
Rational Canonical Form (7.4) |
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第5週 |
3/24,3/26 |
1. Computation of Rational Form.(7.4)
2. Matrix Limits and Exponential (5.3) |
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第6週 |
3/31 |
Inner Product Space and Examples. (6.1)
* Quiz 1 on Wednesday, March 31. |
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第7週 |
4/07,4/09 |
1. Inner Product Space and Examples. (6.1)
2. Properties of Inner Product Space and Normed Space. (6.1)
* Midterm Exam I on Friday, April 9. |
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第8週 |
4/14,4/16 |
1. The Gram-Schmidt Process. (6.2)
2. Orthogonal Complements. (6.2) |
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第9週 |
4/21,4/23 |
1. Riesz Representation Theorem. (6.3)
2. Adjoint Operator. (6.3) |
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第10週 |
4/28,4/30 |
自主學習週 (配合數學系) |
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第11週 |
5/05,5/07 |
1. Normal Operator and Self-adjoint Operator. (6.4)
2. Unitary Operator and Orthogonal Operator. (6.5) |
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第12週 |
5/12,5/14 |
1. Unitary Operator and Orthogonal Operator. (6.5)
2. Orthogonal Projection. (6.6)
3. Spectral Decomposition Theorem. (6.6)
* Quiz 2 on Friday, May 14. |
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第13週 |
5/19,5/21 |
1. Bilinear Forms. (6.8)
2. Dual Spaces. (2.6) |
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第14週 |
5/26,5/28 |
1. Symmetric Bilinear Forms and Diagonalization. (6.8)
2. Skew-symmetric bilinear forms. |
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第15週 |
6/02,6/04 |
1. Orthogonal Group Preserving Bilinear Forms.
2. Cartan-Dieudonne Theorem.
3. Orthogonal Operators on Euclidean Space. (6.11) |
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第16週 |
6/09,6/11 |
1. Symplectic Groups.
2. Hermitian Forms.
3. Dual Spaces. (2.6) |
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第17週 |
6/16,6/18 |
Quotient Spaces.
* Quiz 3 on Friday, June 18. |
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第18週 |
6/23,6/25 |
* Final Exam on Friday, June 25. |
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