Linear Algebra Project

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Choose a topic, and create a project; and using the following applications of linear algebra concepts:
-Complex numbers
-Complex planes
-Complex roots
-Euler’s formula
-Moivre’s Formula
-Linear Transformation
-Eigenvectors and Eigenvalues
-characteristic polynomial
-discrete linear dynamic systems with eigenvectors and complex eigenvalues
-diagonalizable matrices
-complex eigenvalues
-trajectories, phase portraits
-stability
-Markov chains
-differential equations
-matrix exponentials
-applications of differential equations
-orthogonality

I have decided to make this project on a topic of Image. Please create a linear project that uses matrix to do all kinds of processing of image. Use all the matrix operations I wrote in the instruction. Do something like this website.
http://blog.kleinproject.org/?p=588
also this http://graficaobscura.com/matrix/index.html

MATLAB is the software that needs to be used.

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