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Which of the following are true about principal components analysis (PCA)? Assume that no two eigenvectors of the sample covariance matrix have the same eigenvalue.   A: Appending a 1 to the end of every sample point doesn’t change the results of performing PCA (except that the useful principal component vectors have an extra 0 at the end, and there’s one extra useless component with eigenvalue zero).   B: If you use PCA to project d-dimensional points down to j principal coordinates, and then you run PCA again to project those j-dimensional coordinates down to k principal coordinates, with d > j > k, you always get the same result as if you had just used PCA to project the d-dimensional points directly down to k principle coordinates.  C: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing PCA, the principal component directions do not change.   D: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing PCA, the largest eigenvalue of the sample covariance matrix does not change.

Which of the following are true about principal components analysis (PCA)? Assume that no two eigenvectors of the sample covariance matrix have the same eigenvalue.   A: Appending a 1 to the end of every sample point doesn’t change the results of performing PCA (except that the useful principal component vectors have an extra 0 at the end, and there’s one extra useless component with eigenvalue zero).   B: If you use PCA to project d-dimensional points down to j principal coordinates, and then you run PCA again to project those j-dimensional coordinates down to k principal coordinates, with d > j > k, you always get the same result as if you had just used PCA to project the d-dimensional points directly down to k principle coordinates.  C: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing PCA, the principal component directions do not change.   D: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing PCA, the largest eigenvalue of the sample covariance matrix does not change.

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Which of the following are true about principal components analysis (PCA)? Assume that no two eigenvectors
of the sample covariance matrix have the same eigenvalue.
  A: Appending a 1 to the end of every sample point doesn’t change the results of performing PCA (except that
the useful principal component vectors have an extra 0 at the end, and there’s one extra useless component with
eigenvalue zero).
  B: If you use PCA to project d-dimensional points down to j principal coordinates, and then you run PCA again
to project those j-dimensional coordinates down to k principal coordinates, with d > j > k, you always get the same
result as if you had just used PCA to project the d-dimensional points directly down to k principle coordinates.

 C: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing
PCA, the principal component directions do not change.
  D: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performing
PCA, the largest eigenvalue of the sample covariance matrix does not change.

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