Numerical Linear Algebra
Math 526 -- Sections 1 and 2, Fall 2001

Professor Doug Meade
meade@math.sc.edu
Department of Mathematics
University of South Carolina

Table of Contents

Homework Assignments

Date Assigned
 Section
 Page
 Problems
23 Aug     send e-mail to me
28 Aug 1.1 10 # 3, 7, 14, 18, 27, 31, 33
28 Aug 1.2 25 # 2, 6, 11, 16, 21, 23, 26, 27
28 Aug 1.3 36 # 5, 11, 14, 17, 19, 22, 25
30 Aug 1.4 46 # 3, 4, 7, 10, 12, 22, 25, 31
4 Sep 1.5 54 # 5, 8, 13, 16, 21, 23, 29-32, 37
4 Sep 1.6 64 # 7-13, 19, 22, 23, 27, 29, 38a
6 Sep 1.7 73 # 3, 8, 9, 11, 36, 38
11 Sep 1.8 83 # 1, 4, 7, 17, 18, 26, 28, 29
13 Sep 1.9 93 # 5, 7, 8
18 Sep 2.1 107 # 2, 3, 6, 8, 9, 12, 15
18 Sep 2.2 117 # 3, 6, 7a, 9, 10, 17, 29, 32, 35, 37
18 Sep 2.3 123 # 1, 4-6, 16-24
25 Sep Exam 1   Chapter 1 and Sections 2.1--2.3
27 Sep 2.4 130 # 2, 4, 5, 8, 22
2 Oct 2.5 139 # 1, 6, 9, 15, 16, 26
4 Oct 2.6 147 # 1, 4, 5, 8, 12, 17
9 Oct 2.7 153 # 1-4, 5, 7, 13-15
11 Oct 2.8 163 # 2, 4, 5, 8, 9, 11
18 Oct 4.1 217 # 1, 4, 5, 8, 12, 17
23 Oct 4.2 228 # 3, 5, 11, 16, 22, 23, 38
25 Oct 4.3 237 # 1, 2, 3, 5, 6, 14, 16, 17
30 Oct 4.5 255 # 1, 6, 7, 9, 11, 14, 17
30 Oct 4.6 263 # 3, 6, 7, 11, 13, 15, 19, 20
1 Nov 4.4 248 # 2, 6, 9, 13
1 Nov 4.9 290 # 1, 4, 8, 9, 14, 21
6 Nov Exam 2   Chapters 2 and 4
8 Nov 5.1 302 # 1, 8, 10, 15, 17, 21
13 Nov 5.2 311 # 2, 3, 17, 21
13 Nov 5.3 319 # 1, 6, 9, 14, 23, 24
15 Nov 5.8 363 # 1, 7, 11, 19
15 Nov 6.1 376 # 1, 4, 5, 10, 20, 27
20 Nov 6.2 386 # 2, 7, 13, 24, 29
27 Nov 6.3 395 # 1, 7, 13
29 Nov 6.4 402 # 2, 13, 17
29 Nov 6.5 411 # 3, 6, 7, 12, 17, 19, 22
4 Dec 6.6 420 # 2, 8, 11
4 Dec 7.1 448 # 3, 4, 6, 10, 11, 15, 20, 25
13 Nov Final Exam 9:00am-noon Comprehensive

Extra Credit

Extra credit assignments are not discussed in class. I will be glad to talk to you about them individually. I prefer e-mailed solutions but will accept paper submissions. Any Extra Credit points earned will be used where they are most advantageous.

Date Due Points Assignment
27 Nov 10 MATLAB can be used for some rather incredible things. For example, several pictures can be encoded in a single MATLAB image with a clever use of floating point numbers. Execute the following MATLAB statements: 
      id = get(image,'CData');
      id = (id-floor(id))*32;
      image(id);
Repeat the last two commands several times. Provide a complete list of all the different images you see. Explain what is being done in the reassignment of id. What is the maximum number of images that could be stored in this manner?
27 Nov 10 Prove: Halloween = Christmas.
Hint: Write the dates like I do and think about other (number) bases.

Lab Assignments

Date Assigned
 Date Due
 Title
 Text Reference
 Comments
29 Aug 4 Sep Getting Started with MATLAB   good introduction to MATLAB geared towards the needs of this course
29 Aug 4 Sep Practice Row Operations Section 1.2 provides practice obtaining an echelon form of a matrix with row operations using the replace, swap, and scale commands
5 Sep 10 Sep Exchange Economy and Homogeneous Systems Section 1.5 Find equilibrium prices for an exchange economy
5 Sep 10 Sep Population Migration Section 1.9 (Exercise 11) More detailed, and interesting, version of Exercise 11 in Section 1.9 of the text
12 Sep 17 Sep Visualizing Linear Transformations of the Plane Sections 1.7 and 1.8 To understand the standard matrix of a linear transformation, particularly for shears, rotations, reflections, contractions, and extensions.
19 Sep 25 Sep Rank and Linear Independence Section 1.6 To define the rank of a matrix and to learn its connection with linear independence of the columns of a matrix.
26 Sep 2 Oct Using Backslash to Solve Ax=b Section 2.2 To learn about MATLAB's backslash command (\) and why it is preferred over explicit computation of a matrix inverse or Gaussian elimination for solving systems Ax=b when A is invertible.
26 Sep 2 Oct Roundoff Error in Matrix Calculations Section 2.2 Continues the investigation of the previous lab with an emphasis on floating point computations, including an introduction to the condition number of a matrix.
3 Oct 9 Oct Schur Complements Section 2.4 To learn about Schur Complements and their connection with row reduction.
10 Oct 17 Oct LU Factorization Section 2.5 To practice the LU factorization algorithm discussed in the text and to compare this with the results of MATLAB's lu command.
17 Oct 23 Oct An Economy with an Open Sector Section 2.7 More investigation of Leontief Input/Output Models.
17 Oct 23 Oct Matrix Inverses and Infinite Series Section 2.7 To see examples when the inverse of (I-C) can be obtained as an infinite series I + C + C^2 + ... and when this infinite series does not converge to the inverse.
23 Oct 29 Oct Partitioned Matrices Section 2.4 To obtain more experience and familiarity working with partitioned matrices.
30 Oct 6 Nov Subspaces Section 4.1 To obtain a more complete understanding of span, basis, and dimension. In particular, to realized that subspaces with the same dimension are not necessarily equal. This project is good practice for Exam 2.
7 Nov 13 Nov Markov Chains and Long-Range Predictions Sections 2.1 and 4.9 To investigate several Markov chains and to investigate the long-term properties of these problems.
14 Nov 20 Nov Real and Complex Eigenvalues Sections 5.1 and 5.5 To learn how to use MATLAB to find eigenvalues, including complex-valued eigenvalues (and eigenvectors).
28 Nov 4 Dec Using Eigenvalues to Study Spotted Owls Sections 5.1, 5.5, and 5.6 To use eigenvalues to identify the critical juvenile survival rate that guarantees the the long-term success of the spotted owl population.
5 Dec 11 Dec Least Squares Solutions and Curve Fitting Section 6.6 To obtain numerical and graphical experience using least squares to fit experimental data.

MATLAB Diaries

Date Created
 Filename
 Comments
6 Sep 06Sep.txt Exercises from Sections 1.6 and 1.7
11 Sep 11Sep.txt Examples for Sections 1.8
13 Sep 13Sep.txt Solution to Quiz 3 and Example for Section 1.9
4 Oct 04Oct.txt Example of Jacobi and Gauss-Seidel iterative methods and the importance of diagonal dominance (Section 2.6)
9 Oct 09Oct.txt Leontief Input-Output Model Examples (Section 2.7)
11 Oct 11Oct.txt Applications to Computer Graphics (Section 2.8)
Auxiliary files: [letterN.m] [graphic2d.m]
23 Oct 23Oct.txt Example with Nul A and Col A (Section 4.2)
25 Oct 25Oct.txt Examples with bases, column spaces, and null spaces (Section 4.3)
30 Oct 30Oct.txt Examples with bases, column spaces, and null spaces (Section 4.3)
1 Nov 01Nov.txt Applications to Markov Chains (Section 4.9)
1 Nov quiz9.txt Solution to Quiz 9
15 Nov 15Nov.txt Iterative Estimates for Eigenvalues (Section 5.8)
15 Nov 27Nov.txt Orthogonal Matrices and Projections (Sections 6.2 and 6.3)
27 Nov ec1.txt Solution to Extra Credit #1
29 Nov 29Nov.txt Examples with the Gram-Schmidt Process and the QR Factorization (Section 6.4)
4 Dec 04Dec.txt Examples with Linear Models (Section 6.6)
6 Dec 06Dec.txt Examples of Orthogonal Diagonalization (Section 7.1)

Additional Resources

Notes:

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    • If you have any questions, please send e-mail to meade@math.sc.edu
    Last modified: 23 August 2001