6.47.4  Determinant of a matrix: det

The det command finds 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. This requires 2ⁿ operations, but can stil be faster for average sized matrices (up to about n=20).
• det(A ⟨,method⟩) returns the determinant of the matrix A.

Examples.

• Input:
  det([[1,2],[3,4]])
  Output:

  −2

• Input:
  det(idn(3))
  Output:

  1