Spring 2023 Linear Algebra
上課時間: 週三34，週五34.
上課地點: 週三 新生303，周五 新生303
3/15上課筆記 (revised 3/22)
Office hour: 週三 2PM-3PM (地點: 天數412)
Text book: "Matrix theory and linear algebra" by Herstein
and Winter
(You may also look at "Linear algebra" by Friedberg, Insel and
Spence)
Syllabus:
Quotient and dual spaces.
Inner product.
Orthogonal projection.
Orthonormal basis, Gram-Schmidt
process
Hilbert
space,
Riesz representation theorem.
Adjoint of linear transformations. Unitary and
normal operators.
Spectral theory for normal operators.
Applications of linear algebras
Cartan-Dieudonne theorem.
Singular Value Decomposition: Low-rank
approximation; Moore-Penrose inverse and linear
regressions.
Spectral
radius. Perron-Frobenious theorem.
Directed graphs with weights.
PageRank algorithm.
The number of common zeros of two polynomials.
Bezoutiant and resultants.
Bilinear forms and quadratic forms. Witt
decomposition and Witt cancellation.
作業: 1 , 2, 3, 4, 5 , 6, 7, 8, 9, 10
若同學因故
無法上課時, 建議利用數學系2016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)
數學系(B11~), 新生303
姚皓勻 (b07201020
AT g.ntu.edu.tw)
數學系(B11~以外)+物理+資工+機械+土木+外文,
新生301
吳以理 (r11221004 AT
ntu.edu.tw) 其他系所同學, 新生
403
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%) April 12, 10:20---12:30,
範圍約到2016課程錄影的20160406左右
期末考(40%) June 7,
10:20---12:30