5.51.4 Determinant of a matrix : det
det takes as argument a matrix A.
det returns the determinant of the matrix A.
Input :
det([[1,2],[3,4]])
Output :
-2
Input :
det(idn(3))
Output :
1
An optional argument can be used to specify with an optional argument.
-
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).