國立中央大學一百零六學年度下學期線性代數B班課程網頁
宣佈事項：
6/19(二)期末考，範圍：8.D, 10.A, 10.B, note on determinant, diagonalizing a matrix, Jordan canonical form
6/14(四)第十次小考，範圍：Diagonalizing a matrix, Jordan canonical form
6/7(四)第九次小考，範圍：Note on determinant
5/31(四)第八次小考，範圍：10.A, 10.B(1, 2, 3, 4, 5)
5/24(四)第七次小考，範圍：8.D, 10.A(1, 2, 4, 5)
5/10(四)第二次期中考，範圍：7.B, 7.C, 8.A, 8.B, 8.C
5/3(四)第六次小考，範圍：8.A, 8.B
4/26(四)第五次小考，範圍：7.C, 8.A(1, 2, 3, 5, 6, 7)
4/19(四)第四次小考，範圍：7.B
3/29(四)第一次期中考，範圍：6.A, 6.B, 6.C, 7.A
3/22(四)第三次小考，範圍：6.C
3/15(四)第二次小考，範圍：6.B
3/8(四)第一次小考，範圍：6.A
Office hour and Office:
黃榮宗老師：鴻經館418，星期三 1:00-2:00 PM或預約
助教 : 郭昶卲，鴻經館213
課本：
Linear Algebra Done Right, Sheldon Axler, 3rd Ed., Springer, 課本電子書, 課本網頁, 線上課程
參考書：
Linear Algebra, 4th Ed., by Friedberg, Insel, and Spence
課程進度：
Week 1:
2/22: 6.A Inner products and Norms
Week 2:
2/27: 6.A Inner products and Norms
3/1: 6.B Orthonormal bases
Week 3:
3/6: 6.B Orthonormal bases
3/8: 6.C Orthogonal complements and minimization problems
Week 4:
3/13: 6.C Orthogonal complements and minimization problems
3/15: 7.A Self-adjoint and normal operators
Week 5:
3/20: 7.A Self-adjoint and normal operators
3/22: 7.B The spectral theorem
Week 6:
3/27: Review for Midterm 1
3/29: Midterm 1
Week 7:
4/3: 7.B The spectral theorem
4/5: National holiday, no classes
Week 8:
4/10: 7.C Positive operators and isometries
4/12: 7.C Positive operators and isometries
Week 9:
4/17: 8.A Generalized eigenvectors and nilpotent operators
4/19: 8.A Generalized eigenvectors and nilpotent operators
Week 10:
4/24: 8.B Decomposition of an operator
4/26: 8.B Decomposition of an operator
Week 11:
5/1: 8.C Characteristic and minimal polynomials
5/3: 8.C Characteristic and minimal polynomials
Week 12:
5/8: Review for Midterm 2
5/10: Midterm 2
Week 13:
5/15: 8.D Jordan form
5/17: 10.A Trace
Week 14:
5/22: 10.A Trace, 10.B Determinant
5/24: Determinant
Week 15:
5/29: Determinant
5/31: Determinant
Week 16:
6/5: Diagonalizing a matrix
6/7: Jordan canonical form
Week 17:
6/12: Jordan canonical form
6/14: Review for Final
Week 18:
6/19: Final
評量配分比重：
小考20%(最低二次不採計)+第一次期中考25%+第二次期中考25%+期末考30%
授課大綱及建議習題：
Chapter 6. Inner product spaces
6.A Inner Products and Norms 1, 2, 4, 5(Suppose V is finite dimensional), 6-13, 15-17, 19, 20, 22, 24, 25, 27, 28, 31
6.B Orthonormal Bases 1, 2, 3, 5, 6, 7, 8(寫下q的公式即可)
6.C Orthogonal Complements and Minimization Problems 1-6, 8-12
Chapter 7. Operators on inner product spaces
7.A Self-adjoint and Normal Operators 1-9, 12, 14-16, 18, 19
7.B The Spectral Theorem 1-6, 8, 10, 14, 15
7.C Positive Operators and Isometries 1-7, 9, 10, 11, 13
7.D Polar Decomposition and Singular Value Decomposition
Chapter 8. Operators on complex vector spaces
8.A Generalized Eigenvectors and Nilpotent Operators 1, 2, 3, 5, 6, 7, 9, 11, 12, 13, 14
8.B Decomposition of an Operator 1, 2, 3, 5, 6
8.C Characterisitc and Minimal Polynomials 1-6, 8-11
8.D Jordan Form 1-5
Chapter 9. Operators on Real Vector Spaces (if time permits)
Chapter 10. Trace and determinant
10.A Trace 1, 2, 4-7, 10, 13-16, 18
10.B Determinant 1, 2, 3, 4, 5
Notes on determinant: (P.85-86) 3.1-3.12, (P.94-95) 5.1-5.6, (P.96-97) 7.1-7.3
Notes on diagonalizing a matrix, Jordan canonical form
習題解答
舊課程網頁：
一百零六學年度上學期線性代數一課程網頁
一百零一學年度上學期線性代數一課程網頁
一百零一學年度下學期線性代數二課程網頁