I'm struggling to understand why the following statement is not correct:
In PCA, the first principal direction is the eigenvector of the data matrix X with the largest associated eigenvalue.

Is it because it should be called the first principal component instead of the first principal direction?

Hey, I assume it is because in PCA the eigenvectors come from XX.T, since we use the matrix Uk, which basically is made by the first k eigenvectors of XX.T (the ones associated with the highest eigenvalues).

## PCA

Dear TAs,

I'm struggling to understand why the following statement is not correct:

In PCA, the first principal direction is the eigenvector of the data matrix X with the largest associated eigenvalue.

Is it because it should be called the first principal component instead of the first principal direction?

Thank you in advance :)

Hey, I assume it is because in PCA the eigenvectors come from XX.T, since we use the matrix Uk, which basically is made by the first k eigenvectors of XX.T (the ones associated with the highest eigenvalues).

## 2

Genius! You are right! Thank you so much :D

XX.T is the covariance matrix, right? And we are assuming that we have subtracted the mean from each row of X.

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