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課程名稱 |
線性代數一
Linear Algebra(Ⅰ) |
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開課學期 |
108-1 |
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授課對象 |
社會科學院 經濟學系 |
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授課教師 |
余正道 |
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課號 |
ECON5132 |
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課程識別碼 |
323 U2050 |
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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 |
選修 |
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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 |
社科102社科102 |
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備註 |
上課資訊依課號MATH1103訊息為主。限選修ECON課號，方可認定為經濟系選修課。
限學士班三年級以上 或 限碩士班以上 或 限博士班
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081econ5132 |
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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 |
This course provides the first step toward understanding and manipulating abstract algebraic systems. Explicit goals include familiarize with the main characters -- linear spaces (possibly equipped with additional structures), and the relations between them or upon themselves -- linear transformations, kernels, quotients, eigenvalues, 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 |
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預期每週課後學習時數 |
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Office Hours |
每週二 15:30~16:30
每週五 08:10~10:00
每週四 12:30~13:30
每週三 12:30~13:30
每週二 12:30~13:30 備註： Tuesday noon (林自立) and afternoon (林浚沂): Astro-Math 103, Wednesday (余正道): Astro-
Math 461, Thursday (王羿璁):
Astro-Math 548, Friday (呂治鴻): Astro-Math 555 |
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指定閱讀 |
Hoffman and Kunze, Linear Algebra. 2nd edition. 1971.
The PDF-version is available on the website https://archive.org |
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參考書目 |
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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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Week 1 |
9/11 |
Vector spaces, subspaces (§2.1, 2.2) |
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Week 2 |
9/18, 20 |
Linear combinations, linear dependence, bases, dimension (§2.3) |
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Week 3 |
9/25, 27 |
Linear maps (§3.1, part of 3.2, 3.3), Quiz 1 |
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Week 4 |
10/02, 04 |
Coordinates and matrix representations (§§2.4, 3.2, 3.4); TA session is replaced by a lecture |
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Week 5 |
10/09 |
Dual space, transpose (part of §3.5, §3.7) |
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Week 6 |
10/16, 18 |
Double dual, annihilator |
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Week 7 |
10/23, 25 |
Linear equations, Quiz 2 |
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Week 8 |
10/30, 11/01 |
Determinant - uniqueness (parts of §5.2, 5.3) |
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Week 9 |
11/06, 08 |
Determinant - existence (§5.2, 5.3), Midterm |
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Week 10 |
11/13 |
Determinant - properties (§5.4); eigenvalues (§6.2) |
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Week 11 |
11/20, 22 |
Characteristic polynomial, arithmetic multiplicity and geometric multiplicity (§6.2) |
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Week 12 |
11/27, 29 |
T-invariant subspaces, decomposition (§6.4, part of §6.7), Quiz 3 |
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Week 13 |
12/04, 06 |
minimal polynomial, T-conductor, primary decomposition (§6.3, §6.8) |
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Week 14 |
12/11, 13 |
Jordan form: statement and structure (part of §7.3), interlude: inner product, projection |
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Week 15 |
12/18, 20 |
Jordan form: construction, rational form I, Quiz 4 |
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Week 16 |
12/25, 27 |
Rational form II (ch.7) |
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Week 17 |
1/03 |
Final exam |
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