Add matrix inversion algorithm using NumPy (#12657)

* Create matrix_inversion.py

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* Update matrix_inversion.py

* Update matrix_inversion.py

* Update matrix_inversion.py

* Update matrix_inversion.py

* Update matrix_inversion.py

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

linear_algebra/matrix_inversion.py

@@ -0,0 +1,36 @@
+import numpy as np
+
+
+def invert_matrix(matrix: list[list[float]]) -> list[list[float]]:
+    """
+    Returns the inverse of a square matrix using NumPy.
+
+    Parameters:
+    matrix (list[list[float]]): A square matrix.
+
+    Returns:
+    list[list[float]]: Inverted matrix if invertible, else raises error.
+
+    >>> invert_matrix([[4.0, 7.0], [2.0, 6.0]])
+    [[0.6000000000000001, -0.7000000000000001], [-0.2, 0.4]]
+    >>> invert_matrix([[1.0, 2.0], [0.0, 0.0]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Matrix is not invertible
+    """
+    np_matrix = np.array(matrix)
+
+    try:
+        inv_matrix = np.linalg.inv(np_matrix)
+    except np.linalg.LinAlgError:
+        raise ValueError("Matrix is not invertible")
+
+    return inv_matrix.tolist()
+
+
+if __name__ == "__main__":
+    mat = [[4.0, 7.0], [2.0, 6.0]]
+    print("Original Matrix:")
+    print(mat)
+    print("Inverted Matrix:")
+    print(invert_matrix(mat))