BUILT-IN MATHEMATICA SYMBOL

PositiveDefiniteMatrixQ

PositiveDefiniteMatrixQ[m]
tests whether m is a positive definite matrix.

Details Details

PositiveDefiniteMatrixQ[m] gives True if m is explicitly positive definite, and gives False if it is a matrix that is not positive definite.
A Hermitian matrix m is considered positive definite if and only if all its eigenvalues are positive.
PositiveDefiniteMatrixQ works with SparseArray objects.
PositiveDefiniteMatrixQ works for symbolic as well as numerical matrices.

Examples Examples open all close all

Basic Examples (1)Basic Examples (1)

Test if a matrix is explicitly positive definite:

Out[2]=

This means that the quadratic form for all vectors :

Out[3]=

Scope (5)Scope (5)

Generalizations & Extensions (1)Generalizations & Extensions (1)

Properties & Relations (4)Properties & Relations (4)

Possible Issues (1)Possible Issues (1)

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See Also See Also

HermitianMatrixQ Eigenvalues MatrixQ

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