Fall 2022 Linear Algebra


上課時間: 週三34，週五34.
上課地點: 週三 新生303，周五 普通203
Office hour: 週三 2PM-3PM (地點: 天數412)

Text book:
"Matrix theory and linear algebra" by Herstein and Winter

Syllabus:

Week 1: Vector spaces: definitions and examples. Linear independence.  (8.1, 8.2, 8.5, 4.1)
Week 2: Steinitz replacement lemma. Basis and dimensions. (8.3, 8.4)
Week 3: Linear transformations. Rank-Nullity Theorem. (9.1, 9.2, 9.4, 4.4)
Week 4: Matrix representation of linear transforms. (3.9, 9.9)
Week 5: The Gauss elimination and elementary matrices. Traces. (3.3, 3.6, 3.7, 3.8, 5.7)
Week 6: Determinants and adjoint matrices. (The entire Chapter 5)
Week 7: Cramer's rule. Cayley-Hamilton Theorem.  (5.10)
Week 8: Invariant subspaces, direct sum of vector spaces. (9.8, 4.2, 4.5, 4.7)
Week 9: Midterm
Week 10: Eigenspaces, diaogonalization and the application to linear differential equations. (11.5)
Week 11: Jordan form (I). (10.1, 10.2, 10.3)
Week 12: Jordan form (II).
Week 13: Rational form (I).
Week 14: Rational form (II).
Week 15: Exponential of matrices and systems of linear differential equations. (10.4,10.5)

(We shall also use some material in "Linear algebra" by Friedberg, Insel and Spence)
Homework: 1 , 2 , 3, 4, 5 ,6, 7, 8, 9, 10, 11, 12 (revised, Dec 10!)
 
11/18  Jordan form定理證明
10/21  C-H定理證明補充
10/12 上課筆記
10/07 上課筆記
第四次上課 09/23 上課筆記 
第三次上課 09/21 上課筆記
第二次上課 09/14 上課筆記
 
若同學因故無法上課時, 建議利用數學系2015課 程錄影補完相關項目

習題課時 間:  每週五第四節
助教和習題課教室分配
李俊緯 (d09221001AT ntu.edu.tw)     普通203,   數學系
吳以理 (r11221004 AT ntu.edu.tw)     新生301，經濟系+農經系+政治系
姚皓勻 (b07201020 AT g.ntu.edu.tw) 普通504,  其他

評量方式:

作業 (25%) 週五第四節上課前繳交(請利用NTU COOL上傳作業或習題課當面交給助教), 逾期不收。
隔離同學請以將作業以 email在截止日期前寄送給助教，
若因確診身體極度不適無法及時完成作業請務必補醫師證明, 方能補交作業。

期中考(35%) 11/2, 10:20---12:30 範圍約到2015課程錄影的20151030左右

期末考(40%) 12/21, 10:20---12:30 範圍約到Jordan forms和HW11.