線性代數
LINEAR ALGEBRA
李程輝
國立交通大學電信工程學系
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教師及助教資料
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教師：李程輝
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助教：林建成 邱登煌
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Office Room: ED 828
Ext. 31563
Lab: ED 823
E-mail: aircheng.cm94g@nctu.edu.tw ;
s413543.cm94g@nctu.edu.tw
Ext. 54570
課程網址
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http://banyan.cm.nctu.edu.tw/linearalgebra2006
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教科書
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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.
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成績算法
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正式考試3次 (各30%)
作業(10%)
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Several Applications
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How many solutions do Ax  b have?
It may have none, one or infinitely many solutions
depending on rank(A) and whether
b  col ( A) or not.
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How to solve the following Lyapunov and
Riccati equations:
AX  XA  Q  0
A X  XA  XBR B X  Q  0
T
1
T
Matrix Theory
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Find the local extrema of
f :   C
n
2
f  0 & definiteness of the Hessian matrix.
 How to determine the definiteness of a real
symmetric matrix?
eigenvalues
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How to determine the volume of a parallelogram?
Determinant
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How to find the solutions or characterize the
dynamical behaviors of a linear ordinary
differential equation?
Eigenvalues, Eigenvectors
vector space and linear independency
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How to predict the asymptotic( Steady-state)
behavior of a discrete dynamical system ( p280.)
Eigenvalues & Eigenvectors
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 xi 
 Given 
 y , i  1, , n
 i
Find the best line y  C0  C1 xto fit the data.
i.e., find
n

i 1
C0 & C1 
2
yi  (C0  C1 xi ) is minimum
Least Square problem
(Orthogonal projection)
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How to expand a periodic function as sum of
different harmonics? ( Fourier series)
Orthogonal projection
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How to approximate a matrix by as few as data?
Digital Image Processing
Singular Value Decomposition
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How to transform a dynamical system into one
which is as simple as possible?
Diagnolization, eigenvalues and eigenvectors
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How to transform a dynamical system into a
specific form ( e.g., controllable canonical form)
Change of basis
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課程簡介
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Introduction to Linear Algebra
Matrices and Systems of Equations
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Systems of Linear Equations
Row Echelon Form
Matrix Algebra
Elementary matrices
Partitioned Matrices
Determinants
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The Determinants of a Matrix
Properties of Determinants
Cramer’s Rule
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Vector Spaces
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Definition and Examples
Subspace
Linear Independence
Basis and Dimension
Change of Basis
Row Space and Column Space
Linear Transformations
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Definition and Examples
Matrix Representations of Linear
Transformations
Similarity
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Orthogonality
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The Scalar Product of Euclidean Space
Orthogonal Subspace
Least Square Problems
Inner Product Space
Orthonormal Set
Eigenvalues
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Eigenvalues and Eigenvectors
Systems of Linear Differential Equations
Diagonalization
Hermitian Matrices
The Singular Value Decomposition
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Quadratic Forms
Positive Definite Matrices
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Exercise for Chapter 1
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P.11:
P.28:
P.62:
P.76:
P.87:
P.97:
9,10
8,9,10
12,13,21,*22,23,27
3(a,c),*6,12,18,23
*18
Chapter test 1-10
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Exercise for Chapter 2
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P.105:
P.112:
P.119:
P.123:
1,*11
5-8,*10-12
2(a,c),4,7,*8,11,12
Chapter test 1-10
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Exercise for Chapter 3
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P.131:
P.142:
P.154:
P.161:
P.173:
P.180:
P.186:
3-6,13,15
1,*3,5-9,13,14,16-20
5,*7-11,14-17
3,*5,7,9,11,13,15,16
1,4,*7,10,11
3,6-9,12,*13,16,17,19-21
Chapter test 1-10
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Exercise for Chapter 4
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P.195:
P.208:
P.217:
P.221:
1,8,*9,12,16,18-20,23,24
*3,5,11,13,18
*5,7,8,10-15
Chapter test 1-10
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Exercise for Chapter 5
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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
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Exercise for Chapter 6
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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
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