matrix.inverse_of_matrix

Functions

inverse_of_matrix(→ list[list[float]])

A matrix multiplied with its inverse gives the identity matrix.

Module Contents

matrix.inverse_of_matrix.inverse_of_matrix(matrix: list[list[float]]) → list[list[float]]

A matrix multiplied with its inverse gives the identity matrix. This function finds the inverse of a 2x2 and 3x3 matrix. If the determinant of a matrix is 0, its inverse does not exist.

Sources for fixing inaccurate float arithmetic: https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python https://docs.python.org/3/library/decimal.html

Doctests for 2x2 >>> inverse_of_matrix([[2, 5], [2, 0]]) [[0.0, 0.5], [0.2, -0.2]] >>> inverse_of_matrix([[2.5, 5], [1, 2]]) Traceback (most recent call last):

…

ValueError: This matrix has no inverse. >>> inverse_of_matrix([[12, -16], [-9, 0]]) [[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]] >>> inverse_of_matrix([[12, 3], [16, 8]]) [[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]] >>> inverse_of_matrix([[10, 5], [3, 2.5]]) [[0.25, -0.5], [-0.3, 1.0]]

Doctests for 3x3 >>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]]) [[2.0, 5.0, -4.0], [1.0, 1.0, -1.0], [-5.0, -12.0, 10.0]] >>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]]) Traceback (most recent call last):

…

ValueError: This matrix has no inverse.

>>> inverse_of_matrix([[],[]])
Traceback (most recent call last):
    ...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
Traceback (most recent call last):
    ...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2, 1], [0,3, 4]])
Traceback (most recent call last):
    ...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]])
Traceback (most recent call last):
    ...
ValueError: This matrix has no inverse.

>>> inverse_of_matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]