linear_algebra.src.rank_of_matrix

Calculate the rank of a matrix.

See: https://en.wikipedia.org/wiki/Rank_(linear_algebra)

Functions

rank_of_matrix(→ int)

Finds the rank of a matrix.

Module Contents

linear_algebra.src.rank_of_matrix.rank_of_matrix(matrix: list[list[int | float]]) → int

Finds the rank of a matrix.

Args:

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]]
>>> 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
>>> rank_of_matrix([[2,3,-1,-1],
...                [1,-1,-2,4],
...                [3,1,3,-2],
...                [6,3,0,-7]])
4
>>> rank_of_matrix([[2,1,-3,-6],
...                [3,-3,1,2],
...                [1,1,1,2]])
3
>>> rank_of_matrix([[2,-1,0],
...                [1,3,4],
...                [4,1,-3]])
3
>>> rank_of_matrix([[3,2,1],
...                [-6,-4,-2]])
1
>>> rank_of_matrix([[],[]])
0
>>> rank_of_matrix([[1]])
1
>>> rank_of_matrix([[]])
0