determinant

Topics

• linear algebra
• matrices

The determinant of a square matrix is a scalar value that represents the “volume” or scaling factor of the linear transformation represented by the matrix. It’s denoted as $\det (A)$ or $|A|$.

• The determinant of a matrix is the product of its eigenvalues
• A determinant of 1 means the transformation preserves the area or volume
• A determinant of 0 indicates that the matrix cannot be inverted

from numpy.linalg import det
 
A = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
d = det(A)  # ≈ 0 (singular)

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