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9/ 19/13 Readi ngs | Li near Algebra | Mathematics | MIT OpenCourseWare ocw.mit.edu/courses/mathemat ics/ 18-06- l inear -algebra-spri ng-2010/readi ngs/ 1/ 3 OCW needs your opinion. Please take a moment to complete this survey. Your feedback will help us improve MIT OpenCourseWare.  Subscribe to the OCW Newsletter Enter Email Help | Contact Us Search Advanced Search Home » Courses » Mathematics » Linear Algebra » Readings Readings COURSE HOME SYLLABUS CALENDAR READINGS ASSIGNMEN  TS EXAMS STUDY MATERIALS  TOOLS RELATED RESOURCES VIDEO LECTURES DOWNLOAD COURSE MATERIALS The readings are assigned in: Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 978098 0232714 . The T able of Contents is listed below. SES # TOPICS READINGS 1 The geometry of linear equations 1.1-2.1 2 Eliminat ion with mat ri ce s 2.2-2.3 3 Matrix operations and inverses 2.4-2.5 4 LU and LDU fac tori zat ion 2.6 5 Tr ansp oses and per muta tion s 2.7 6 Vector spaces and subspaces 3.1 7 The nullspace: Solving Ax = 0 3.2 8 Rectangular PA = LU and Ax = b 3.3-3.4 9 Row reduced echelon form 3.3-3.4 10 Basis and dimension 3.5 11 The four fundamental subspaces 3.6 12 Exam 1: Chapt ers 1 to 3. 4 13 Graphs and networks 8.2 14 Orthogonality 4.1 15 Projections a nd subspaces 4.2 16 Le as t squ ar es appro xim atio ns 4. 3 17 Gram-S chmi dt and A = QR 4.4 18 Pr ope rties of dete rmi nants 5.1 19 Fo rm u las for determi na nts 5.2 20 Appl ications of determi nant s 5. 3 21 Ei genvalues and ei gen ve ctors 6 .1 22 Diagonalization 6.2 23 Markov matrices 8.3 24 Review for exam 2  25 Exam 2: Chapters 1-5, 6.1- 6.2, 8.2  26 Differential equations 6.3 27 Symmetric matrices 6.4 28 Positive de finite mat rices 6.5 Courses About Donate Featured Sites

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Page 1: Readings LinearAlgebra MathematicsMITOpenCourseWare

7/27/2019 Readings LinearAlgebra MathematicsMITOpenCourseWare

http://slidepdf.com/reader/full/readings-linearalgebra-mathematicsmitopencourseware 1/3

9/19/13 Readings | Linear Algebra | Mathematics | MIT OpenCourseWare

ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/readings/

OCW needs your opinion. Please take a moment to complete this survey. Your feedback will help

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Home » Courses » Mathematics » Linear Algebra » Readin

Readings

COURSE HOME

SYLLABUS

CALENDAR

READINGS

ASSIGNMEN TS

EXAMS

STUDY MATERIALS

 TOOLS

RELATED RESOURCES

VIDEO LECTURES

DOWNLOAD COURSEMATERIALS

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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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

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9/19/13 Readings | Linear Algebra | Mathematics | MIT OpenCourseWare

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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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