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【免费提供】Introduction_to_Linear_Algebra_5th_Gilbert_Strang
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【免费提供】Introduction_to_Linear_Algebra_5th_Gilbert_Strang这是线性代数的经典原版英文教材。
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INTRODUCTI N
TO
LINEAR ALGEBRA
Fifth Edition
GILBERT STRANG
Massachusetts Institute of Technolo
WELLESLEY - CAMBRIDGE PRESS
Box 812060 Wellesley MA 02482
E
typesetting by Ashley Feandes
9876543
Wavelets and Filter Banks,
= A.
=
=
= + = + =
Table
of
Contents
1 Introduction to Vectors
1
1.1
Vectors and Linear Combinations . 2
1.2
Lengths and Dot Products .
11
1.3
Matrices .
...
..
...
22
2 Solving Linear Equations
31
2.1
Vectors and Linear Equations .
31
2.2
The Idea
of
Elimination . . .
46
2.3
Elimination Using Matrices .
58
2.4
Rules for Matrix Operations
70
2.5
Inverse Matrices . . . . . . .
83
2.6 Elimination = Factorization: A =
LU
97
2.7
Transposes and Permutations .
..
.
..
109
3
Vector Spaces and Subspaces
123
3.1
Spaces
of
Vectors . . . . . . .
............
123
3.2
The Nullspace
of
A: Solving
Ax
= 0 and
Rx
= 0
135
3.3
The Complete Solution to
Ax
= b .
150
3.4
Independence, Basis and Dimension
164
3.5
Dimensions
of
the Four Subspaces
181
4 Orthogonality
194
4.1 Orthogonality
of
the Four Subspaces
194
4.2
Projections
...
.
..
. .
..
...
206
4.3
Least Squares Approximations . . .
219
4.4
Orthonormal Bases and Gram-Schmidt .
233
5
Determinants
247
5.1
The Properties
of
Determinants .
247
5.2 Permutations and Cofactors . . .
258
5.3 Cramer's Rule, Inverses, and Volumes
273
iii
iv
6 Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues . .
6.2 Diagonalizing a Matrix . . . .
6.3
Systems
of
Differential Equations
6.4
Symmetric Matrices . . . . . . . .
6.5
Positive Definite Matrices . . . . .
7 The Singular Value Decomposition (SVD)
7
.1
Image Processing by Linear Algebra . . . .
7 .2 Bases and Matrices in the
SVD . . . . . . .
7 .3
Principal Component Analysis (PCA
by
the SVD) .
7.4 The Geometry
of
the SVD . . . . . . . . . . . . .
8 Linear Transformations
8.1 The Idea
of
a Linear Transformation
8.2 The Matrix
of
a Linear Transformation .
8.3 The
Search for a Good Basis . .
..
. .
9 Complex Vectors and Matrices
9.1 Complex Numbers
.....
.
9.2 Hermitian and Unitary Matrices
9.3 The Fast Fourier Transform .
10 Applications
10.l
Graphs and Networks .
...
.
...
..
..
.
10.2 Matrices in Engineering . . . . . . . . . . . .
10.3 Markov Matrices, Population, and Economics
10.4 Linear Programming
..........
. . .
10.5 Fourier Series: Linear Algebra for Functions .
10.6 Computer Graphics . . . . . . . .
10.7 Linear Algebra for Cryptography
..
.
...
.
11
Numerical Linear Algebra
11
.1 Gaussian Elimination in Practice
11.2 Norms and Condition Numbers .
11.3 Iterative Methods and Preconditioners
12 Linear Algebra
in
Probability & Statistics
12.1 Mean, Variance, and Probability . . . . . .
12.2 Covariance Matrices and Joint Probabilities
12.3 Multivariate Gaussian and Weighted Least
Squares
Matrix Factorizations
Index
Six Great Theorems I Linear Algebra
in
a Nutshell
Table
of
Contents
288
288
304
319
338
350
364
364
371
382
392
401
401
411
421
430
431
438
445
452
452
462
474
483
490
496
502
508
508
518
524
535
535
546
555
563
565
574
Preface
(amazin
g
).
(and the video lecture
s
).
Julia Python,
S
end
s
u
gg
e
s
tion
s
to
V
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