[FAQ Bot] UPDATE: np.linalg.inv(XTX) throws LinAlgError: Singular matrix — what does this

_questions/machine-learning-zoomcamp/module-2/003_0a7e9c723a_linalgerror-singular-matrix.md

@@ -1,9 +1,19 @@
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 id: 0a7e9c723a
-question: 'LinAlgError: Singular matrix'
+question: 'np.linalg.inv(XTX) throws LinAlgError: Singular matrix — what does this
+  mean?'
 sort_order: 3
 ---
 
-It’s possible that when you follow the videos, you’ll get a Singular Matrix error. This will be explained in the Regularization video. Don’t worry, it’s normal to encounter this.
+A `LinAlgError: Singular matrix` from `np.linalg.inv(XTX)` means `XTX` is not invertible—typically because its rows/columns are linearly dependent (often due to redundant features or insufficient independent information).
 
-You might also receive this error if you invert matrix `X` more than once in your code.
+To diagnose, check whether the matrix is rank-deficient:
+
+- Compute `np.linalg.matrix_rank(XTX)` and compare it to the number of columns of `XTX` (if the rank is smaller, it’s singular).
+
+Common fixes:
+
+- Drop or combine redundant features so you get a full-rank `XTX`.
+- Instead of the exact inverse, use the pseudo-inverse: `np.linalg.pinv(XTX)`. The pseudo-inverse works even when the matrix is singular, and is often the preferred approach in ML when you can’t guarantee full rank.
+
+If you still get the error, also verify you’re forming `XTX` correctly (e.g., for linear regression it should be based on `X.T @ X`, not `X @ X.T`).