Cross validation works with testing the algorithms to know which one is the best, the testing is done by doing n-fold cross validation.
We use the mean value fo Y to calculate the error becaus we can calculate the standard deviation from it
Eigen values of a symmetric matrix are always real
It was called Eigendecompostion all the time
In PCA we calculate the covaraince of our very high imensional data, lets say 5 dimensions, then we calculate the eigendecomposition, i.e we get the eigen vectors for our fitted gaussian, after that we use these eigenv ectors to project our data to principle components (the eigen vectors with the largest eigen values or with the largest variance, or the ones that have most information about data)
After projecting the data to subspace now I can use these projected features in creating models.
Reference: PCA lecture from MIT OpenCourseWare introduction to neural computation.