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...

1

線性代數LINEAR ALGEBRA

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. 31563

助教：林建成 邱登煌 Lab: ED 823 E-mail: aircheng.cm94g@nctu.edu.tw ;

s413543.cm94g@nctu.edu.tw Ext. 54570

課程網址 http://banyan.cm.nctu.edu.tw/linearalgebra2006

3

教科書

Textbook: S.J. Leon, Linear Algebra with Applications, 7th Ed., Prentice Hall, 2006.

Reference: R. Larson and B.H. Edwards, Elementary Linear Algebra, 4th 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.)(Acolb

bxA

6

How to solve the following Lyapunov and Riccati equations:

Matrix Theory

0 QXAAX

01 QXBXBRXAXA TT

7

Find the local extrema of

definiteness of the Hessian matrix. How to determine the definiteness of a real

symmetric matrix?

eigenvalues

2: Cf n

&0f

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)

niy

x

i

i ,,1,

xCCy 10

10 &CC2

110 )(

n

iii xCCy

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