Fix sphinx/build_docs warnings for linear_algebra (#12483)

* Fix sphinx/build_docs warnings for linear_algebra/

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

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

linear_algebra/src/gaussian_elimination_pivoting.py

@@ -6,17 +6,18 @@ def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
     Solve a linear system of equations using Gaussian elimination with partial pivoting
 
     Args:
-    - matrix: Coefficient matrix with the last column representing the constants.
+      - `matrix`: Coefficient matrix with the last column representing the constants.
 
     Returns:
-    - Solution vector.
+      - Solution vector.
 
     Raises:
-    - ValueError: If the matrix is not correct (i.e., singular).
+      - ``ValueError``: If the matrix is not correct (i.e., singular).
 
     https://courses.engr.illinois.edu/cs357/su2013/lect.htm Lecture 7
 
     Example:
+
     >>> A = np.array([[2, 1, -1], [-3, -1, 2], [-2, 1, 2]], dtype=float)
     >>> B = np.array([8, -11, -3], dtype=float)
     >>> solution = solve_linear_system(np.column_stack((A, B)))

linear_algebra/src/rank_of_matrix.py

@@ -8,11 +8,15 @@ See: https://en.wikipedia.org/wiki/Rank_(linear_algebra)
 def rank_of_matrix(matrix: list[list[int | float]]) -> int:
     """
     Finds the rank of a matrix.
+
     Args:
-        matrix: The matrix as a list of lists.
+        `matrix`: The matrix as a list of lists.
+
     Returns:
         The rank of the matrix.
+
     Example:
+
     >>> matrix1 = [[1, 2, 3],
     ...            [4, 5, 6],
     ...            [7, 8, 9]]

linear_algebra/src/schur_complement.py

@@ -12,13 +12,14 @@ def schur_complement(
 ) -> np.ndarray:
     """
     Schur complement of a symmetric matrix X given as a 2x2 block matrix
-    consisting of matrices A, B and C.
-    Matrix A must be quadratic and non-singular.
-    In case A is singular, a pseudo-inverse may be provided using
-    the pseudo_inv argument.
+    consisting of matrices `A`, `B` and `C`.
+    Matrix `A` must be quadratic and non-singular.
+    In case `A` is singular, a pseudo-inverse may be provided using
+    the `pseudo_inv` argument.
+
+    | Link to Wiki: https://en.wikipedia.org/wiki/Schur_complement
+    | See also Convex Optimization - Boyd and Vandenberghe, A.5.5
 
-    Link to Wiki: https://en.wikipedia.org/wiki/Schur_complement
-    See also Convex Optimization - Boyd and Vandenberghe, A.5.5
     >>> import numpy as np
     >>> a = np.array([[1, 2], [2, 1]])
     >>> b = np.array([[0, 3], [3, 0]])

linear_algebra/src/transformations_2d.py

@@ -3,13 +3,15 @@
 
 I have added the codes for reflection, projection, scaling and rotation 2D matrices.
 
+.. code-block:: python
+
     scaling(5) = [[5.0, 0.0], [0.0, 5.0]]
-  rotation(45) = [[0.5253219888177297, -0.8509035245341184],
-                  [0.8509035245341184, 0.5253219888177297]]
-projection(45) = [[0.27596319193541496, 0.446998331800279],
-                  [0.446998331800279, 0.7240368080645851]]
-reflection(45) = [[0.05064397763545947, 0.893996663600558],
-                  [0.893996663600558, 0.7018070490682369]]
+    rotation(45) = [[0.5253219888177297, -0.8509035245341184],
+                    [0.8509035245341184, 0.5253219888177297]]
+    projection(45) = [[0.27596319193541496, 0.446998331800279],
+                      [0.446998331800279, 0.7240368080645851]]
+    reflection(45) = [[0.05064397763545947, 0.893996663600558],
+                      [0.893996663600558, 0.7018070490682369]]
 """
 
 from math import cos, sin