15.1.4  Determinant of a matrix

The det and det_minor commands compute the determinant of a matrix.

• det takes one mandatory argument and one optional argument:
  • A, a matrix.
  • Optionally, method, which determines how the determinant will be computed and can be one of:
    • lagrange When the matrix elements are polynomials or rational functions, this method computes the determinant by evaluating the elements and using Lagrange interpolation.
    • rational_det This method uses Gaussian elimination without converting to to the internal format for fractions.
    • bareiss This uses the Gauss-Bareiss algorithm.
    • linsolve This uses the p-adic algorithm for matrices with integer coefficients.
    • minor_det This uses expansion by minor determinants, which requires 2ⁿ operations, but can still be faster for average sized matrices (up to about n=20).
• det(A ⟨,method ⟩) returns the determinant det(A) of the matrix A.

Examples

The det_minor command finds the determinant of a matrix by expanding the determinant using Laplace’s algorithm.

• det_minor takes A, a matrix.
• det_minor(A) returns the determinant det(A) of the matrix A.

Examples