Added rank of matrix in linear algebra

linear_algebra/src/Rank_of_Matrix.py

@@ -0,0 +1,67 @@
+"""This is a python program that calculates the rank of a matrix"""
+""" BY - RUDRANSH BHARDWAJ"""
+
+
+def rank_of_matrix(matrix: list[list]) -> int:
+    """
+    Finds the rank of a matrix.
+
+    Args:
+        matrix (list of lists): The matrix as a list of lists.
+
+    Returns:
+        int: The rank of the matrix.
+
+    Example:
+    >>> matrix1 = [[1, 2, 3],
+    ...            [4, 5, 6],
+    ...            [7, 8, 9]]
+    >>> rank_of_matrix(matrix1)
+    2
+    >>> matrix2 = [[1, 0, 0],
+    ...            [0, 1, 0],
+    ...            [0, 0, 0]]
+    >>> rank_of_matrix(matrix2)
+    2
+    >>> matrix3 = [[1, 2, 3, 4],
+    ...            [5, 6, 7, 8],
+    ...            [9, 10, 11, 12]]
+    >>> rank_of_matrix(matrix3)
+    2
+    """
+
+    rows = len(matrix)
+    columns = len(matrix[0])
+    rank = min(rows, columns)
+
+    for row in range(rank):
+        # Check if diagonal element is not zero
+        if matrix[row][row] != 0:
+            # Eliminate all the elements below the diagonal
+            for col in range(row + 1, rows):
+                multiplier = matrix[col][row] / matrix[row][row]
+                for i in range(row, columns):
+                    matrix[col][i] -= multiplier * matrix[row][i]
+        else:
+            # Find a non-zero diagonal element to swap rows
+            reduce = True
+            for i in range(row + 1, rows):
+                if matrix[i][row] != 0:
+                    matrix[row], matrix[i] = matrix[i], matrix[row]
+                    reduce = False
+                    break
+            if reduce:
+                rank -= 1
+                for i in range(rows):
+                    matrix[i][row] = matrix[i][rank]
+
+            # Reduce the row pointer by one to stay on the same row
+            row -= 1
+
+    return rank
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()