linalg(deprecated)/definite - Maple Help

linalg(deprecated)

 definite
 test for positive or negative definite matrices

 Calling Sequence definite(A, kind)

Parameters

 A - square symmetric matrix kind - one of the following symbols: 'positive_def', 'positive_semidef', 'negative_def', or 'negative_semidef'

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(2,2,\left[2,1,1,3\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{2}& {1}\\ {1}& {3}\end{array}\right]$ (1)
 > $\mathrm{definite}\left(A,'\mathrm{positive_def}'\right)$
 ${\mathrm{true}}$ (2)
 > $B≔\mathrm{array}\left(1..2,1..2,'\mathrm{symmetric}'\right):$
 > $\mathrm{definite}\left(B,'\mathrm{negative_semidef}'\right)$
 ${{B}}_{{1}{,}{1}}{\le }{0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{and}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{-}{{B}}_{{1}{,}{1}}{}{{B}}_{{2}{,}{2}}{+}{{B}}_{{1}{,}{2}}^{{2}}{\le }{0}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{and}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{{B}}_{{2}{,}{2}}{\le }{0}$ (3)