This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

HermitianMatrixQ

HermitianMatrixQ[m]
tests whether m is a Hermitian matrix.
Test if a matrix is explicitly Hermitian:
For a real matrix, this is equivalent to symmetry:
Test if a matrix is explicitly Hermitian:
In[1]:=
Click for copyable input
Out[1]=
For a real matrix, this is equivalent to symmetry:
In[2]:=
Click for copyable input
Out[2]=
HermitianMatrixQ works with SparseArray objects:
HermitianMatrixQ works with symbolic matrices:
All symbolic quantities are assumed to be complex:
Use a different method for Hermitian matrices:
Construct complex-valued matrices for testing:
For the non-Hermitian complex-valued matrix m, the function just uses Gaussian elimination:
For the Hermitian indefinite matrix mi, the function tries the Cholesky method first:
For the Hermitian positive definite matrix mp, the function succeeds with the Cholesky method:
HermitianMatrixQ[m] is effectively equivalent to m==ConjugateTranspose[m]:
Hermitian matrices have all real eigenvalues:
This also means that their characteristic polynomials have real coefficients:
New in 6