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- Application of Linear Algebra - possible project topics
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Here are some potential topics for your project/paper on an application of linear algebra. So far these are all taken from the textbook. I’ll be post more topics over the next couple days, so check back on this thread.
But in any case take a look at these sections of the textbook to get an idea of the wide variety of linear algebra applications. Looks through the examples as well as the exercises:
1.6: applications in economics, chemistry, network flows
1.10: linear algebra models for nutrition, electrical networks, population/migration (difference equations)
2.6: more about the economics “input-output” model introduced in Sec 1.6 (actually first introduced in the intro to Ch 1)
2.7: applications to computer graphics
4.8: more on difference equations – applications to signal processing/filtering
4.9: Markov chains (more on migration models, including a voting model)
5.6: Discrete dynamical systems (primary example is a predator-prey model)
5.7: Applications to differential equations
6.6: Linear models (statistics – regression; examples from various application domains)
6.8: Applications of inner product spaces (more statistics)
7.5: Image processing (and even more statistics)
Note that some of these sections include “Further Reading” references (2.7, 4.8, 5.6, 6.6, 7.5)
if we choose to do this project when will it be due
Since I announced this relatively recently, I’ll give you as long as possible. You can hand in your writeup (2-3 pages) before taking the final exam.
Though I’d like to get a 1-paragraph description of what topic you’ve chosen this week. I’ll discuss in class tomorrow.
Here is the book chapter introducing linear algebra techniques for image deblurring–another potential project topic:
http://www.siam.org/books/fa03/FA03Chapter1.pdf
A few links about the linear algebra behing Google PageRank algorithm:
http://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf
http://www.ams.org/samplings/feature-column/fcarc-pagerank
http://www.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html
A set of slides on the linear algebra of image compression:
http://math.arizona.edu/~brio/VIGRE/ThursdayTalk.pdf
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