1 線性代數 LINEAR ALGEBRA 李程輝 國立交通大學電信工程學系

2 教師及助教資料 教師：李程輝 Office Room: ED 828 Ext 助教：林建成 邱登煌 Lab: ED ; Ext 課程網址

3 教科書 Textbook: S.J. Leon, Linear Algebra with Applications, 7 th Ed., Prentice Hall, Reference: R. Larson and B.H. Edwards, Elementary Linear Algebra, 4 th Ed., Houghton Mifflin Company, 2000.

4 成績算法 正式考試 3 次 ( 各 30%) 作業 (10%)

5 Several Applications How many solutions do have? It may have none, one or infinitely many solutions depending on rank(A) and whether or not.

6 How to solve the following Lyapunov and Riccati equations: Matrix Theory

7 Find the local extrema of definiteness of the Hessian matrix. How to determine the definiteness of a real symmetric matrix? eigenvalues

8 How to determine the volume of a parallelogram? Determinant

9 How to find the solutions or characterize the dynamical behaviors of a linear ordinary differential equation? Eigenvalues, Eigenvectors vector space and linear independency

10 How to predict the asymptotic( Steady-state) behavior of a discrete dynamical system ( p280.) Eigenvalues & Eigenvectors

11 Given Find the best line to fit the data. i.e., find is minimum Least Square problem (Orthogonal projection)

12 How to expand a periodic function as sum of different harmonics? ( Fourier series) Orthogonal projection

13 How to approximate a matrix by as few as data? Digital Image Processing Singular Value Decomposition

14 How to transform a dynamical system into one which is as simple as possible? Diagnolization, eigenvalues and eigenvectors

15 How to transform a dynamical system into a specific form ( e.g., controllable canonical form) Change of basis

16 課程簡介 Introduction to Linear Algebra Matrices and Systems of Equations Systems of Linear Equations Row Echelon Form Matrix Algebra Elementary matrices Partitioned Matrices Determinants The Determinants of a Matrix Properties of Determinants Cramer’s Rule

17 Vector Spaces Definition and Examples Subspace Linear Independence Basis and Dimension Change of Basis Row Space and Column Space Linear Transformations Definition and Examples Matrix Representations of Linear Transformations Similarity

18 Orthogonality The Scalar Product of Euclidean Space Orthogonal Subspace Least Square Problems Inner Product Space Orthonormal Set Eigenvalues Eigenvalues and Eigenvectors Systems of Linear Differential Equations Diagonalization Hermitian Matrices The Singular Value Decomposition

19 Quadratic Forms Positive Definite Matrices

20 Exercise for Chapter 1 P.11: 9,10 P.28: 8,9,10 P.62: 12,13,21,*22,23,27 P.76: 3(a,c),*6,12,18,23 P.87: *18 P.97: Chapter test 1-10

21 Exercise for Chapter 2 P.105: 1,*11 P.112: 5-8,*10-12 P.119: 2(a,c),4,7,*8,11,12 P.123: Chapter test 1-10

22 Exercise for Chapter 3 P.131: 3-6,13,15 P.142: 1,*3,5-9,13,14,16-20 P.154: 5,*7-11,14-17 P.161: 3,*5,7,9,11,13,15,16 P.173: 1,4,*7,10,11 P.180: 3,6-9,12,*13,16,17,19-21 P.186: Chapter test 1-10

23 Exercise for Chapter 4 P.195: 1,8,*9,12,16,18-20,23,24 P.208: *3,5,11,13,18 P.217: *5,7,8,10-15 P.221: Chapter test 1-10

24 Exercise for Chapter 5 P237: 6,7,10,*13,14. P247: 2,9,11,*13,14,16. P258: *5,7,9,10,12 P267: 4,8,9,26,*27,28,29 P286: 2,4,*12~14,16,19,22,23,25,33 P297: 3~5,12,*4 P310: Chapter test 1~10

25 Exercise for Chapter 6 P323 : 2~16, 18, *19, 22~*25, 27 P351 : 1 (a)*(e), 4, 6, 7, 9~12, 16~18, 23(b), 24(a), 25~28 P363 : 8, 10~*13, *19, 21 P380 : *5, 6 P395 : 3(a)(b), 7(a)(b), 8~14, *12 P403 : *3, 8~13 P421 : Chapter test 1~10