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本課程已開放可以加簽,如還有需要加簽(電機系與電資院學生班優先),請於本週內(9/19)上網簽選。

線性代數第一週採用線上上課,第一次上課時間是9月15號。
上課時間:每週三,週五 10:10-12:10
上課鏈接:https://meet.google.com/mbh-ttns-gvf
如果疫情許可,第二週起將採線上/線下混合授課。詳情,請見第一次上課說明。

相關課程教材,可由國立清華大學 eeclass 數位學習平台取得。


RK
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課程大綱
Course Introduction,
– Part I: Vectors Spaces and Linear Transformations

W27; Vector, Vector Space, Subspace, Chap. 1
W27; Linear Combinations, Systems of Linear Equations, Chap. 1
W27; Linear Dependence and Linear Independence, Chap. 1
W27; base and Dimension, Chap. 1
W27; Maximal Linearly Independent Subsets, Chaps. 1
W27; Linear Transformations, Null Space, and Range, Chap. 2
W27; Matrix Representation, Chap. 2
W27; Composition, Invertibility and Isomorphisms, Chap. 2
W27; Change of Coordinate Matrix, Chap. 2
W27; Dual Spaces, Chap. 2
W27; Midterm Exam I

– Part II: Matrix and Determinant W27; Matrix Operations, Chap. 3

W27; Rank of a Matrix, Chap. 3 W27; Matrix Inverse, Chap. 3
W27; Determinants, Chap. 4
W27; Eigenvalue and Eigenvector, Chap. 5
W27; Diagonalizability Chap. 5
W27; Invariant Subspace Chap. 5
W27; Cayley-Hamilton Theorem, Chap. 5
W27; Inner Product and Norm, Chap. 6
W27; Gram-Schmidt Orthogonalization Process, Chap. 6

Midterm Exam II

– Part III: Diagonalization and Inner Product Space
W27; Adjoint of a Linear Operator, Chap. 6
W27; Normal, Self-Adjoint, Unitary, and Orthogonal Operators, Chap.6
W27; Spectral Theorem, Chap. 6
W27; Bilinear and Quadratic Forms, Chap. 6
W27; Jordan form
W27; Complex Hilbert Space
W27; Final Exam

教科書
Text Book: Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence, “Linear Algebra,” 4th Edition
(Prentice- Hall).

Reference Book: Gilbert Strang, “Introduction to Linear Algebra,” international 5th Edition (Wellesley-
Cambridge Press).

成績說明
1. Assignments (after every lecture)

2. In-class Quiz (> 12): 40%; (every Friday morning, 10:10-10:40 AM)
3. Midterm I: 20%; (TBD, To Be Determined)
4. Midterm II: 20%; (TBD, To Be Determined)
5. Final Exam: 20% (TBD, To Be Determined)