Deep understanding of PCA

I want to learn PCA in depth, initial questions which I want to address are:

1. What is Eigen Vector, Eigen Values and Eigen Matrix?

2. How we extract Eigen Vector and Values (good examples)

3. How PCA preserve similarities (distances)?

4. How curse of dimensionality affect PCA?

5. How PCA extract High variance in the first PC components?

6. What normalization techniques we use to normalize the data before PCA?

7. What are projections?

8. What are pros and cons of PCA?

9. A small working example of PCA in any good analysis software like excel to elaborate the concepts

10. I also want to know some good applications of PCA.

Skills: Algorithm, C++ Programming, Machine Learning, Mathematics, Statistics

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