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7/27/2019 Readings LinearAlgebra MathematicsMITOpenCourseWare
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9/19/13 Readings | Linear Algebra | Mathematics | MIT OpenCourseWare
ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/readings/
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The readings are assigned in: Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge PresFebruary 2009. ISBN: 978098 0232714 . The Table of Contents is listed below.
SES # TOPICS READINGS
1The geometry of linearequations
1.1-2.1
2 Elimina tion with ma tr ice s 2.2-2.3
3Matrix operations andinverses
2.4-2.5
4 LU and LDU fa ctor iza tion 2.6
5 T ra ns po se s a nd p er muta tio ns 2.7
6 V ec to r s pa ce s a nd sub sp ace s 3.1
7 The nullspace: Solving Ax = 0 3.2
8Rectangular PA = LU and Ax= b
3.3-3.4
9 Row reduced echelon form 3.3-3.4
10 Basis and dimension 3.5
11The four fundamentalsubspaces
3.6
12 Exam 1: Chapters 1 to 3.4
13 Graphs and networks 8.2
14 Orthogonality 4.1
15 Proje ctions a nd subspa ce s 4.2
16 Le as t s qu ar es appro xim atio ns 4 .3
17 G ra m-S chm idt a nd A = QR 4.4
18 P ro pe rtie s o f d ete rm ina nts 5.1
19 Fo rm ula s fo r d ete rm ina nts 5.2
20 A pplic ati on s o f dete rm in an ts 5 .3
21 E igen valu es and e igen ve cto rs 6 .1
22 Diagonalization 6.2
23 Markov matrices 8.3
24 Review for exam 2
25Exam 2: Chapters 1-5, 6.1-6.2, 8.2
26 Differential equations 6.3
27 Symmetric matrices 6.4
28 Positiv e de finite ma trices 6.5
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7/27/2019 Readings LinearAlgebra MathematicsMITOpenCourseWare
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9/19/13 Readings | Linear Algebra | Mathematics | MIT OpenCourseWare
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Course Study Group
In section 2.4 #11,can someone helpme understand whythe answer to b) BA= 4B is B=0? Idon't see how thezero matrix over Ayields 4 time… 2replies
the number of different nxnsymmetric matriceswith 4 elementswhere a!=b!=c!=d
1 reply
Find an elementf(x) of the span of {sin x, 1} in thevector space F(R)such that f(x)>0 forall x 1 reply
Guys can anyonehelp me how tomake linear algebrainteresting? Our sironly expects proofsand it is verydifficult ...Anysuggestions?? 2replies
29 Matrices in engineering 8.1
30 Similar matrices 6.6
31 S in gu lar v alu e dec om po si ti on 6 .7
32Fourier series, FFT, complexmatrices
8.5, 10.2-10.3
33 Linear transformations 7.1-7.2
34 Choice of basis 7.3
35 Linear programming 8.4
36 Course review
37Exam 3: Chapters 1-8 (8.1, 2,3, 5)
38 Nume rica l line ar a lge bra 9.1-9.3
39 Computational scienceSee the Web site for18.085
40 Final exam
Table of Contents
1. Introduction to Vectors
1.1 Vectors and Linear Combinations1.2 Lengths and Dot Products1.3 Matrices
2. Solving Linear Equations
2.1 Vectors and Linear Equations2.2 The Idea of Elimination2.3 Elimination Using Matrices2.4 Rules for Matrix Operations2.5 Inverse Matrices2.6 Elimination = Factorization: A = LU2.7 Transposes and Permutations
3. Vector Spaces and Subspaces
3.1 Spaces of Vectors3.2 The Nullspace of A: Solving Ax = 03.3 The Rank and the Row Reduced Form3.4 The Complete Solution to Ax = b3.5 Independence, Basis, and Dimension3.6 Dimensions of the Four Subspaces
4. Orthogonality
4.1 Orthogonality of the Four Subspaces4.2 Projections4.3 Least Squares Approximations4.4 Orthogonal Bases and Gram-Schmidt
5. Determinants
5.1 The Properties of Determinants5.2 Permutations and Cofactors5.3 Cramer's Rule, Inverses, and Volumes
6. Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues6.2 Diagonalizing a Matrix6.3 Applications to Differential Equations6.4 Symmetric Matrices
6.5 Positive Definite Matrices6.6 Similar Matrices6.7 Singular Value Decomposition (SVD)
7. Linear Transformations
7.1 The Idea of a Linear Transformation7.2 The Matrix of a Linear Transformation7.3 Diagonalization and the Pseudoinverse
8. Applications
8.1 Matrices in Engineering8.2 Graphs and Networks8.3 Markov Matrices, Population, and Economics8.4 Linear Programming8.5 Fourier Series: Linear Algebra for Functions8.6 Linear Algebra for Statistics and Probability8.7 Computer Graphics
9. Numerical Linear Algebra
7/27/2019 Readings LinearAlgebra MathematicsMITOpenCourseWare
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9/19/13 Readings | Linear Algebra | Mathematics | MIT OpenCourseWare
ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/readings/
9.1 Gaussian Elimination in Practice9.2 Norms and Condition Numbers9.3 Iterative Methods and Preconditioners
10. Complex Vectors and Complex Matrices
10.1 Complex Numbers10.2 Hermitian and Unitary Matrices10.3 The Fast Fourier Transform
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