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課程名稱 |
線性代數二
Linear Algebra (Ⅱ) |
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開課學期 |
107-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
莊武諺 |
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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/1072MATH1104 |
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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 1,2,3,4,5,7 of [FIS]. In this semester we will start from chapter 6 of [FIS]. |
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課程目標 |
See above. |
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課程要求 |
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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 |
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參考書目 |
[FIS] Linear Algebra, 4th Edition
by Stephen Friedberg, Arnold Insel, and Lawrence Spence
Other references will be supplemented along the way. |
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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. |
作業 |
20% |
4~6 homework assignments. |
2. |
小考 |
20% |
4 quizzes. |
3. |
Midterm |
30% |
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4. |
Final |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/20,2/22 |
2/20: dual spaces.
2/22: dual spaces, quotient spaces.
2/23: no class. |
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第2週 |
2/27,3/01 |
2/27: dual spaces, quotient spaces.
3/01: no class. |
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第3週 |
3/06,3/08 |
3/06: inner product space.
3/08: Gram-Schmidt process, orthogonal projection. |
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第4週 |
3/13,3/15 |
3/13: orthogonal projection, Hilbert space, 小考一
3/15: Hilbert space, Riesz Representation Theorem. |
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第5週 |
3/20,3/22 |
3/20: adjoint of linear transformations.
3/22: normal and self-adjoint operators. |
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第6週 |
3/27,3/29 |
3/27: orthogonal and unitary operators. 小考二
3/29: orthogonal and unitary operators, positive (semi)definite operators. |
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第7週 |
4/03,4/05 |
4:03: no class.
4/05: no class. |
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第8週 |
4/10,4/12 |
4/10: orthogonal projection.
4/12: spectral theorem, simultaneous diagonalization. |
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第9週 |
4/17,4/19 |
4/17: midterm.
4/19: singular value decomposition, polar decomposition. |
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第10週 |
4/24,4/26 |
4/24: pseudoinverse.
4/26: pseudoinverse, bilinear forms. |
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第11週 |
5/01,5/03 |
5/1: bilinear forms.
5/3: quadratic forms. |
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第12週 |
5/08,5/10 |
5/08: quadratic forms, 小考三
5/10: quadratic spaces. |
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第13週 |
5/15,5/17 |
5/15: Witt decomposition theorem.
5:17: Witt cancellation theorem. |
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第14週 |
5/22,5/24 |
5/22: Cartan-Dieudonne theorem, 小考四
5/24: Cartan-Dieudonne theorem, Bezoutians and Resultants. |
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第15週 |
5/29,5/31 |
5:29: Bezoutians and Resultants.
5/31: Bezout theorem. |
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第16週 |
6/05,6/07 |
6/05: final.
6/07: no class. |
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