Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[Determinant], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function det computes the determinant of the given matrix.

The second argument (optional) specifies that the computational method of minor expansion should be used.  This works well for sparse matrices.

With no extra argument, a decision is made automatically whether to use minor expansion or Gaussian elimination (or a combination of both). Specifying the extra argument eliminates the overhead of the decision process if you happen to know ahead of time that minor expansion will work best.

The command with(linalg,det) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{hilbert}\left(3\right)$

$A≔\left[\begin{array}{ccc}1& \frac{1}{2}& \frac{1}{3}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{4}\\ \frac{1}{3}& \frac{1}{4}& \frac{1}{5}\end{array}\right]$

$\det \left(A\right)$

$\frac{1}{2160}$

$B≔\mathrm{matrix}\left(2\,2\right)$

$B≔\left[\begin{array}{cc}{\mathrm{`?`}}_{1,1}& {\mathrm{`?`}}_{1,2}\\ {\mathrm{`?`}}_{2,1}& {\mathrm{`?`}}_{2,2}\end{array}\right]$

$\det \left(B\right)$

$B_{1,1}{B}_{2,2}-B_{1,2}{B}_{2,1}$