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

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

For numerical matrices, definite returns true if the matrix has the property specified by the parameter kind. The properties are positive definite, positive semidefinite, negative definite, or negative semidefinite.

For matrices with non-numerical entries, definite returns a conjunction of Boolean expressions, all of which must be true if the matrix is to have the property specified by the parameter kind.

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

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

$A≔\mathrm{matrix}\left(2\,2\,\left[2\,1\,1\,3\right]\right)$

$A≔\left[\begin{array}{cc}2& 1\\ 1& 3\end{array}\right]$

$\mathrm{definite}\left(A\,'\mathrm{positive\_def}'\right)$

$\mathrm{true}$

$B≔\mathrm{array}\left(1..2\,1..2\,'\mathrm{symmetric}'\right)\:$

$\mathrm{definite}\left(B\,'\mathrm{negative\_semidef}'\right)$

$B_{1,1}\le 0\mathbf{and}-B_{1,1}{B}_{2,2}+B_{1,2}^2\le 0\mathbf{and}{B}_{2,2}\le 0$