You're welcome! I'm glad I could help. To answer your question, yes, the output for the projected data and the transformation matrix are both NumPy arrays. The projected data has the same shape as the original data, except the number of features is reduced to the number of components you choose to keep. The transformation matrix has the shape (n_features, n_components), where each column is a principal component vector. You can use the NumPy dot function to perform the matrix multiplication between the centered data and the transformation matrix to get the projected data. For example:

```python
# Choose the number of components to keep
n_components = 2

# Get the transformation matrix by slicing the principal components array
transformation_matrix = principal_components[:, :n_components]

# Project the centered data onto the transformation matrix
projected_data = np.dot(data_centered, transformation_matrix)
```
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