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課程名稱 |
線性代數二
Linear Algebra (Ⅱ) |
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開課學期 |
110-2 |
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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/1102MATH1104 |
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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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課程影片連結：
https://www.youtube.com/channel/UCTtzslMAs5ZHzvDI5eOOxbQ/videos |
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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 |
每週五 13:30~14:30 備註： office hour 地點：天數403 |
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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 |
30% |
原則上每週都有作業 |
2. |
midterm |
35% |
4/6(Wed) |
3. |
final |
35% |
6/1(Wed) |
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週次 |
日期 |
單元主題 |
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第1週 |
2/16,2/18 |
2/16: dual spaces.
2/18: quotient spaces. |
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第2週 |
2/23,2/25 |
2/23: inner product space.
2/25: inner product space, Gram-Schmidt process. |
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第3週 |
3/02,3/04 |
3/02: orthogonal projection.
3/04: Hilbert space, Riesz representation theorem. |
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第4週 |
3/09,3/11 |
3/09: Riesz representation theorem.
3/11: adjoint operators, normal operators. |
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第5週 |
3/16,3/18 |
3/16: normal and self-adjoint operators.
3/18: positive (semi)definite, orthogonal and unitary operators. |
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第6週 |
3/23,3/25 |
3/23: orthogonal and unitary operators.
3/25: orthogonal projection, spectral theorem. |
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第7週 |
3/30,4/01 |
3/30: spectral theorem, simultaneous diagonalization of normal operators.
4/01: singular value decomposition, polar decomposition. |
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第8週 |
4/06,4/08 |
4/06: midterm.
4/08: pseudoinverse. |
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第9週 |
4/13,4/15 |
4/13: pairs of commuting matrices over a finite field.
4/15: pairs of commuting matrices over a finite field. |
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第10週 |
4/20,4/22 |
4/20: bilinear forms.
4/22: bilinear forms, quadratic forms. |
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第11週 |
4/27,4/29 |
4/27: quadratic forms.
4/29: quadratic spaces. |
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第12週 |
5/04,5/06 |
5:04: quadratic spaces.
5/06: Witt decomposition theorem. |
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第13週 |
5/11,5/13 |
5/11: Cartan-Dieudonne theorem.
5/13: Cartan-Dieudonne theorem. |
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第14週 |
5/18,5/20 |
5/18: Bezout theorem.
5/20: Bezout theorem. |
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第15週 |
5/25, 5/27 |
5/25: no class.
5/27: no class. |
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第16週 |
6/01,6/03 |
6/01: final. |
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