Error Messages/41278

Example Messsage

Array is not Hermitian in function Decompose.  A Hermitian matrix 
is one that is equal to its own conjugate transpose, i.e., the element 
in the ith row and jth column is equal to the complex conjugate of 
the entry in the jth and ith column.

Cause

You have passed a matrix to the system function Decompose (or to a user-defined function that uses Decompose, such as Gaussian), that contains at least one complex (non-real) number and that is not Hermitian. Hermitian basically means non-symmetric as it usually applies to matricies containing complex numbers (when a matrix contains all real-valued numbers, the concept of Hermitian is the same as the concept of being symmtrical). The Cholesky decomposition of a matrix can only be obtained for a Hermitian matrix.

A Hermitian matrix, A, indexed by I and J, is a matrix with the following property:

A = ComplexConjugate(Transpose(A,I,J))

Stated differently, this means that for any element:

RealPart(A[I=m,J=n]) = RealPart(A[J=m,I=n])
ImPart(A[I=m,J=n]) = -ImPart(A[J=m,I=n])

The diagonal elements are all real numbers.

See Also

• Hermitian matrices
• Complex Numbers

See Also

• Decompose