Python Determinant of a Matrix
import numpy as np
from numpy.linalg import det
2x2 Example
matrix = np.array([[4, 7], [2, 6]])
matrix_det = det(matrix)
print(matrix_det)
3x3 Example
matrix = np.array([[3, 8, 1], [4, 6, 9], [7, 5, 2]])
matrix_det = det(matrix)
print(matrix_det)
singular matrix
matrix_singular = np.array([[8, 4], [4, 2]])
matrix_det_singular = det(matrix_singular)
print(matrix_det_singular)
if np.isclose(np.linalg.det(matrix_singular), 0):
print("Matrix is singular, inverse cannot be computed.")
else:
np.linalg.inv(matrix_singular)
identity matrix
I = np.identity(3)
det_I = np.linalg.det(I)
print(det_I)
The determinant of a product of matrices satisfies det(AB)=det(A)⋅det(B)
A = np.array([[2, 1], [3, 4]])
det_A = np.linalg.det(A)
print(det_A)
B = np.array([[0, 5], [6, 7]])
det_B = np.linalg.det(B)
print(det_B)
det_AB = np.linalg.det(np.dot(A, B))
print(det_AB)
Swapping two rows (or columns) of a matrix multiplies the determinant by − 1
A_swapped = np.array([[3, 4], [2, 1]]) # Swap rows of A
det_A_swapped = np.linalg.det(A_swapped)
print(det_A_swapped)
Eigenvalues of A and their product
eigenvalues_A, _ = np.linalg.eig(A)
eigenvalues_product = np.prod(eigenvalues_A)
print(eigenvalues_product)
Scale A by a scalar k and compute determinant
k = 3
scaled_A = k * A
print(A)
print(scaled_A)
det_scaled_A = np.linalg.det(scaled_A)
print(det_scaled_A)
print(det_A)
the shape attribute of a numpy array provides the dimensions of the array as a tuple
scaled_det = (k ** A.shape[0]) * det_A
A.shape[0]
print(scaled_det)
python determinant without numpy
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