Principal Component Analysis, Covariance Matrices, and Eigenvectors

PLEASE FOLLOW ALL THE DIRECTIONS BELOW STEP BY STEP TO WRITE THE RESEARCH PAPER. 
Formatting:

– Make sure you either write mathematical expressions by a math-typesetting program (such as LaTex). For example, your paper should not include “x^2” but rather x2. 

  1. Include a title page with the following information: 
    1. the title of your project.
  2. Include an introduction to your project. Make sure to include the following information:
    • An abstract (at least 50 words)
    • A brief history of the problem (at least 50 words)
      • When did researchers become interested in this type of problem?
      • What strategies were first used to solve this type of problem?
      • How was the strategy that you are using developed?
    • The field in which you are applying linear algebra methods to
    • An explanation of the importance of the problem and why you are particularly interested in it (at least 50 words)
  3. Summary of how you used linear algebra to solve your chosen problem (at least 50 words)
    • Include the names of all methods and theorems used. 
  4. Present the solution to your problem (approximately 2-3 pages). Make sure to include:
    • A statement preceding each computation explaining why the computation is necessary and where each piece of the computation comes from. Students should be able to read this statement and then understand how to replicate this computation for a similar exercise.
    • A concluding statement following each computation interprets the result in context.
  5. Include a conclusion (at least 50 words). Include the following information
    • Summarize the answer to your problem
    • Any insights you may have had while working on the project
    • An unanswered question (or questions) related to your problem that you leave for the reader to explore.
    • Your conclusion must include an unanswered question for your reader to ponder after learning about your project. This question should be fairly specific and maybe something you are interested in exploring further but did not have time to yet. The question should build on your work, and the reader should at least have a starting point in regards to answering this question after reading your work. 
  6. Works Cited.
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