NumPy: Compute the determinant of a given square array
4. Determinant of a Square Array
Write a NumPy program to compute the determinant of a given square array.
From Wikipedia: In linear algebra, the determinant is a value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. Geometrically, it can be viewed as the scaling factor of the linear transformation described by the matrix.
In the case of a 2 × 2 matrix the determinant may be defined as:
Sample Solution:
Python Code :
import numpy as np
from numpy import linalg as LA
# Create a 2x2 array 'a'
a = np.array([[1, 0], [1, 2]])
# Display the original 2x2 array 'a'
print("Original 2-d array")
print(a)
# Compute the determinant of the 2-D array 'a' using np.linalg.det()
print("Determinant of the said 2-D array:")
print(np.linalg.det(a))
Sample Output:
Original 2-d array [[1 0] [1 2]] Determinant of the said 2-D array: 2.0
Explanation:
The above NumPy code calculates the determinant of a 2x2 matrix.
from numpy import linalg as LA: This line imports the linalg module from NumPy and aliases it as LA. The linalg module contains various linear algebra functions, such as calculating determinants, solving linear equations, etc.
a = np.array([[1, 0], [1, 2]]): This line creates a 2x2 matrix a represented as a NumPy array:
print(np.linalg.det(a)): This line calculates the determinant of the matrix a using the det function from the linalg module (imported as LA). The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as (a * d) - (b * c). In this case, the determinant of matrix a is (1 * 2) - (0 * 1) = 2. Finally print() function prints the result to the console.
For more Practice: Solve these Related Problems:
- Compute the determinant of a square matrix using np.linalg.det and test it on a singular matrix.
- Validate that the determinant of a triangular matrix equals the product of its diagonal elements.
- Compute the determinant of a complex square matrix and compare it with expected analytical results.
- Compare the determinant computed via LU decomposition with that from np.linalg.det for a given matrix.
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