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HermitianMatrixQ
Eigenvalues
MatrixQ
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New in 6.0: Matrix & Linear Algebra Functions
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PositiveDefiniteMatrixQ
PositiveDefiniteMatrixQ
[
m
]
tests whether
m
is a positive definite matrix.
MORE INFORMATION
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
CLOSE ALL
Basic Examples
(1)
Test if a matrix is explicitly positive definite:
In[1]:=
In[2]:=
Out[2]=
This means that the quadratic form
for all vectors
:
In[3]:=
Out[3]=
Scope
(5)
Generalizations & Extensions
(1)
Properties & Relations
(4)
Possible Issues
(1)
SEE ALSO
HermitianMatrixQ
Eigenvalues
MatrixQ
MORE ABOUT
Matrices and Linear Algebra
New in 6.0: Matrix & Linear Algebra Functions
New in 6
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Scope 