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