Inverse of Matrix

inverse_matrix(matrix)

Generate the inverse matrix of a given matrix

Parameters

matrix (list of lists of int or float) – List of lists of numbers representing a matrix

Raises

  • TypeError – First argument must be a 2-dimensional list

  • TypeError – Elements nested within first argument must be integers or floats

  • ValueError – First argument must contain the same amount of lists as the amount of elements contained within its first list

Returns

inverse – List of lists corresponding to the inverse of the original matrix; if original matrix has a determinant of zero, then 0.0001 will be used as its determinant, ensuring a result

Return type

list of lists of float

See also

matrix_of_cofactors(), matrix_of_minors(), transposed_matrix(), linear_determinant(), scalar_product_matrix(), system_solution()

Notes

  • Original matrix: \(\mathbf{A} = \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \cdots & \cdots & \cdots & \cdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix}\)

  • Inverse of matrix: \(\mathbf{A}^{-1} = \frac{1}{|\mathbf{A}|}\cdot{{{\mathbf{A}^M}^C}^T}\)

  • Inverse of a Matrix

Examples

Import inverse_matrix function from regressions library
>>> from regressions.matrices.inverse import inverse_matrix
Generate the inverse of [[1, 2], [3, 4]]
>>> inverse_2x2 = inverse_matrix([[1, 2], [3, 4]])
>>> print(inverse_2x2)
[[-2.0, 1.0], [1.5, -0.5]]
Generate the inverse of [[2, 3, 5], [7, 11, 13], [17, 19, 23]]
>>> inverse_3x3 = inverse_matrix([[2, 3, 5], [7, 11, 13], [17, 19, 23]])
>>> print(inverse_3x3)
[[-0.07692307692307693, -0.3333333333333333, 0.20512820512820512], [-0.7692307692307692, 0.5, -0.11538461538461538], [0.6923076923076923, -0.16666666666666666, -0.01282051282051282]]