This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Det

 Det[m]gives the determinant of the square matrix m.
• Det[m, Modulus->n] computes the determinant modulo n.
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 Scope   (3)
Use exact arithmetic to compute the determinant:
Use machine arithmetic:
Use 40-digit precision arithmetic:
Determinant of a complex-valued matrix:
Determinant of a sparse matrix:
 Options   (1)
Compute a determinant using arithmetic modulo 47:
This is faster than computing Mod:
 Applications   (2)
Cramer's rule for solving a linear system :
For numerical systems,LinearSolve is much faster and more accurate:
Modular computation of a determinant:
Modular determinants:
Recover result:
Shift residue to be symmetric:
CharacteristicPolynomial[m] is equal to :
The determinant is the product of the eigenvalues:
The determinant of a triangular matrix is the product of its diagonal elements:
The determinant of a matrix product is the product of the determinants:
The determinant of the inverse is the reciprocal of the determinant:
Determinants of tridiagonal matrices:
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