矩陣分析
本課程是由 國立陽明交通大學應用數學系 提供。
The purpose of this course is to acquaint the students with some basic concepts in linear algebra and matrix analysis, which are most useful in applications. We will cover (1) the unitary-equivalence, similarity and congruence invariants of finite square matrices, (2) spectral properties of finite matrices, (3) Perron-Frobenius theory of nonnegative matrices, and numerical ranges of finite matrices.
課程用書：
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
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| 授課老師 | 應用數學系 吳培元老師 |
|---|---|
| 課程學分 | 3學分 |
| 授課年度 | 100學年度 |
| 授課對象 | 碩士班學生 |
| 預備知識 | Undergraduate linear algebra |
| 課程提供 | 課程影音 課程綱要 課程行事曆 |
課程目標
The purpose of this course is to acquaint the students with some basic concepts in linear algebra and matrix analysis, which are most useful in applications. We will cover
(1) the unitary-equivalence, similarity and congruence invariants of finite square matrices,
(2) spectral properties of finite matrices,
(3) Perron-Frobenius theory of nonnegative matrices, and numerical ranges of finite matrices.
課程章節
| 內容綱要 |
| General introduction of the course |
| Basic operations on 2-by-2 matrices |
| Row-equivalence, column-equivalence and unitary equivalence of matrices |
| Similarity of matrices |
| Jordan canonical form and spectral properties of matrices |
| Rational form and nonderogatory matrices |
| QR decomposition and singular value decomposition of matrices |
| Perron-Frobenius theory of nonnegative matrices |
| Discussions on mid-term homework problems |
| Matrix inequalities |
| Numerical ranges of matrices |
| Matrix dilations |
| Numerical ranges of matrices |
課程書目
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
評分標準
| 項目 | 百分比 |
| 上課表現、出席率 | 1/3 |
| 期中作業 | 1/3 |
| 期末作業 | 1/3 |
本課程行事曆提供課程進度與考試資訊參考。
學期週次 | 上課日期 | 參考課程進度 |
第一週 | 09/14 |
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| 第二週 | 09/19, 09/21 |
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| 第三週 | 09/26, 09/28 |
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| 第四週 | 10/03, 10/05 |
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| 第五週 | 10/12 |
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| 第六週 | 10/17, 10/19 |
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| 第七週 | 10/24, 10/26 |
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| 第八週 | 10/31, 11/02 |
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| 第九週 | 11/07, 11/09 |
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| 第十週 | 11/14, 11/16 |
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| 第十一週 | 11/21, 11/23 |
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| 第十二週 | 11/28, 11/30 |
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| 第十三週 | 12/05, 12/07 |
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| 第十四週 | 12/12, 12/14 |
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| 第十五週 | 12/19, 12/21 |
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| 第十六週 | 12/26, 12/28 |
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| 第十七週 | 01/02, 01/04 |
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