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Lecture
42 (F 12/06):
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Review
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Lecture
41 (W 12/04):
|
Convergence
of the PageRank algorithm
- Read Sections Page Rank Algorithm and Perron-Frobenius
Theorem in the Supplemental Notes.
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Lecture
40 (M 12/02):
|
The
Singular Value Decomposition (SVD) and classification
- Read Chapter 13 of the course notes and Section\ SVD and
Classification in the Supplemental Notes.
- Matlab code for classification of handwritten
digits digit_classify.m.
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(F
11/29):
|
Thanksgiving
break
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Lecture
39 (W 11/27):
|
The
Singular Value Decomposition (SVD) and data compression
- Read Chapter 13 of the course notes and Section SVD and Data
Compression\ in the Supplemental Notes.
- Matlab code for image compression via the SVD implot.m.
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Lecture
38 (M 11/25):
|
The
Singular Value Decomposition (SVD) and the solution of regularized linear
least squares problems
- Read Chapter 13 of the course notes and Section Regularized Linear
Least Squares Problems and the SVD in the Supplemental Notes.
- Matlab code for regularized linear least
squares via SVD lls_pert_reg.m
and initial_cond_est.m.
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Lecture
37 (F 11/22):
|
The
Singular Value Decomposition (SVD), the Fundamental Theorem of Linear
Algebra, and the solution of linear least squares problems
- Read Chapter 13 of the course notes and Section The Singular Value
Decomposition in the Supplemental Notes.
- Matlab code for linear least squares via SVD lls_pert.m.
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Lecture
36 (W 11/20):
|
The
Singular Value Decomposition (SVD)
- Read Chapter 13 of the Course Notes and Section The Singular Value
Decomposition in the Supplemental Notes.
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Lecture
35 (M 11/18):
|
The
Jordan Normal Form
- Read Section The Jordan Normal Form in the Supplemental Notes.
- Matlab code for the reaction system reaction_ode_eig.m.
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Lecture
34 (F 11/15):
|
Dynamical
systems: Application to mechanical systems
-Read Section Dynamical Systems: Mechanical Systems in the
Supplemental Notes.
- Matlab: spring_ode.m
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Lecture
33 (W 11/13):
|
Diagonalization of matrices and the solution of dynamical systems
- Read Section Diagonalization of
Matrices and the Solution of Dynamical Systems in the Supplemental
Notes.
- Matlab: dyn_sys_ex.m
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Lecture
32 (M 11/11):
|
Diagonalization of symmetric matrices; solution of linear systems;
pseudo inverse
- Read Sections Diagonalization of
Symmetric Matrices and Diagonalization
of Matrices and the Solution of Linear Systems in the Supplemental
Notes.
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Lecture
31 (F 11/08):
|
Diagonalization of symmetric matrices
- Read Section Diagonalization of
Symmetric Matrices in the Supplemental Notes.
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Lecture
30 (W 11/06):
|
Basic
properties of eigenvalues and eigenvectors
-Read Sections Section Basic Properties of Eigenvectors and Eigenvalues
in the Supplemental Notes.
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Lecture
29 (M 11/04):
|
Overview
of eigenvalues and eigenvectors; properties of eigenvalues and eigenvectors
-Read Sections Sections Overview of
Eigenvectors and Eigenvalues and Eigenvectors and Eigenvalues in
the Supplemental Notes.
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Lecture
28 (F 11/01):
|
Dynamical
systems.
-Read Sections Dynamical Systems and Overview of Eigenvectors and
Eigenvalues in the Supplemental Notes.
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Lecture
27 (W 10/30):
|
Complex
Numbers
- Read Section 9.1 of the course notes.
- Read Section Complex Numbers in the Supplemental Notes.
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Lecture
26 (M 10/28):
|
Gram-Schmidt,
QR Decomposition
- Read Section 6.4 of the Course Notes and Section Gram-Schmidt Orthogonalization and QR-Decomposition in the
Supplemental Notes.
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Lecture
25 (F 10/25):
|
Gram-Schmidt
Orthogonalization
- Read Section 6.4 of the Course Notes and Section Gram-Schmidt Orthogonalization and QR-Decomposition in the
Supplemental Notes.
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Lecture
24 (W 10/23):
|
Projections
- Read Section 6.3 in the Course Notes and the Projections section
in the Supplemental Notes.
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Lecture
23 (M 10/21):
|
Applications
of Linear Least Squares Problems; Projections
- Read Section 6.2 in the Course Notes and the Linear Least Squares
section in the Supplemental Notes.
- MATLAB demo: findfiber.m
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Lecture
22 (F 10/18):
|
Applications
of Linear Least Squares Problems
- Read Section 6.2 in the Course Notes and the Linear Least Squares
section in the Supplemental Notes.
- MATLAB demo: findfiber.m
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Lecture
21 (W 10/16):
|
Linear
Least Squares Problems
- Read Sections 6.1 and 6.2 in the Course Notes and the Linear Least
Squares section in the Supplemental Notes.
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|
(M
10/14):
|
Fall
Recess
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Lecture
20 (F 10/11):
|
Vector
Spaces and Linear Transformations
- Read Section 5.3 in the Course Notes and the Vector Space section
in the Supplemental Notes.
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Lecture
19 (W 10/9):
|
Vector
Spaces and Linear Transformations
- Read Section 5.3 in the Course Notes and the Vector Space section
in the Supplemental Notes.
- MATLAB demo: bvp_FEM.m.
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Lecture
18 (M 10/7):
|
Vector
Spaces and Linear Transformations
- Read Section 5.3 in the Course Notes and the Vector Space section
in the Supplemental Notes.
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Lecture
17 (F 10/4):
|
Fundamental
Theorem of Linear Algebra: Application to Trusses
- Read Sections 5.1 and 5.2 in the Course Notes and the Fundamental
Theorem of Linear Algebra section in the Supplemental Notes.
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Lecture
16 (W 10/2):
|
Fundamental
Theorem of Linear Algebra
- Read Sections 5.1 and 5.2 in the Course Notes and the Fundamental
Theorem of Linear Algebra section in the Supplemental Notes.
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Lecture
15 (M 9/30):
|
Basis
and Dimension of a Subspace
- Read Section 4.3 in the Course Notes, and the Range and Null Space
section in the Supplemental Notes.
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|
Lecture
14 (F 9/27):
|
Basis
of a subspace, computing bases of the column space and of the null space
- Read Sections 4.1-4.3 in the Course Notes and the Range and Null Space
section in the Supplemental Notes.
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|
Lecture
13 (W 9/25):
|
The
column space and the null space
- Read Sections 4.1 and 4.2 in the Course Notes and the Range and Null
Space section in the Supplemental Notes.
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|
Lecture
12 (M 9/23):
|
Planar
truss
- Read Section 3.3 in the Course Notes and the Planar Trusses
section in the Supplemental Notes.
- MATLAB demos: fiber.m
for the 3x3 tissue in Figure 3.5
- MATLAB demos: truss.m,
stiff.m for the
truss in the supplemental notes. transmission_tower.m.
- MATLAB demo driver_bracket_truss_optim_lp.m for a structural
optimization problem.
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|
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|
Lecture
11 F 9/20 ):
|
Simple
planar truss; existence of solutions, null space of A
- Read Section 3.3 in the Course Notes and the Planar Trusses
section in the Supplemental Notes.
- MATLAB demos: fiber.m
for the 3x3 tissue in Figure 3.5
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|
|
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|
Lecture
10 (W 9/18):
|
Existence
of the matrix inverse; simple planar truss
- Read Section 3.3 in the Course Notes and the Matrix Inverse
section in the Supplemental Notes.
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|
|
|
|
|
Lecture
9 (M 9/16):
|
LU-decomposition
- Read Sections 3.1, 3.2, pages 33-37 of the Course Notes and the LU-Decomposition
section in the Supplemental Notes.
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|
|
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|
Lecture
8 (F 9/13):
|
Computation
of the matrix inverse; determinant of a matrix
- Read Sections 3.1, 3.2, pages 31-37 of the Course Notes and the Matrix
Inverse and Determinant sections in the Supplemental Notes.
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|
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|
|
Lecture
7 (W 9/11):
|
Gaussian
elimination; matrix inverse
- Read Sections 3.1, 3.2, pages 31-37 in the Course Notes and the Gaussian
Elimination section in the Supplemental Notes.
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|
Lecture
6 (M 9/9):
|
Networks
with resistors and batteries; matrix model of a mass spring system
- Read Chapter 2, pages 21-23 in the Course Notes and the Electrical
Circuits section in the Supplemental Notes.
- Read Chapter 3.1, pages 31, 32 in the Course Notes.
- MATLAB demos: fib2.m and ladder.m. Additional
reading:
- Matrix
Analysis of the Branched Dendrite Nerve Fiber.
|
|
|
|
|
|
Lecture
5 (F 9/6):
|
Matrix
models of resistor networks
- Read Chapter 2, pages 19+20 of the Course Notes and the Electrical
Circuits section in the Supplemental Notes.
- MATLAB demo fib1.m.
|
|
|
|
|
|
Lecture
4 (W 9/4):
|
Google
PageRank
- Read the Google PageRank section in the Supplemental Notes.
- MATLAB demo pagerank_demo1.m.
Additional reading:
- Chapter 7 Google PageRank in Cleve Moler's
E-book Experiments
with MATLAB and the corresponding MATLAB
code (click on the Functions tab and look for pagerank).
- The original papers The anatomy of a
large-scale hypertextual Web search engine by
S. Brin and L. Page, and The PageRank Citation Ranking:
Bringing Order to the Web by L. Page, S. Brin,
R.Motwani, and T. Winograd.
|
|
|
|
(M
9/2):
|
Labor
Day; Rice closed.
|
|
Lecture
3 (F 8/30):
|
Review
of matrix operations
Google PageRank
- Read the Google PageRank section in the Supplemental Notes.
- MATLAB demo pagerank_demo1.m.
Additional reading:
- Chapter 7 Google PageRank in Cleve Moler's
E-book Experiments
with MATLAB and the corresponding MATLAB
code (click on the Functions tab and look for pagerank).
- The original papers The anatomy of a
large-scale hypertextual Web search engine by
S. Brin and L. Page, and The PageRank Citation Ranking:
Bringing Order to the Web by L. Page, S. Brin,
R.Motwani, and T. Winograd.
|
|
|
|
|
|
Lecture
2 (W 8/28):
|
Review
of matrix-vector and matrix-matrix multiplication
- Read Chapter 1 of the Course Notes.
|
|
|
|
|
|
Lecture
1 (M 8/26):
|
Course
overview; review of vectors, basic operations, norms.
- Read Chapter 1 of the Course Notes
|