[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 +1,20 @@
 ---
 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.
+`np.linalg.inv` raises `LinAlgError: Singular matrix` when `XTX` is not invertible, which happens when some columns of `X` are linearly dependent (duplicated or redundant features).
 
-You might also receive this error if you invert matrix `X` more than once in your code.
+It's normal to hit this while following the Module 2 videos. The regularization lesson fixes it by adding a small value to the diagonal before inverting:
+
+```python
+XTX = X.T @ X
+XTX = XTX + r * np.eye(XTX.shape[0])
+w_full = np.linalg.inv(XTX) @ X.T @ y
+```
+
+To diagnose it, compare `np.linalg.matrix_rank(XTX)` with `XTX.shape[0]`. A smaller rank means redundant columns that you can drop or combine. `np.linalg.pinv` avoids the error, but for homework use `inv` with regularization as in the lessons, because the answer options were computed that way.
+
+Also check that you compute `X.T @ X` (not `X @ X.T`) and that you don't invert the matrix twice.