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. Non-Hermitian basically means non-symmetric as it usually applies to matrices containing complex numbers (when a matrix contains all real-valued numbers, the concept of Hermitian is the same as the concept of being symmetrical). 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.

Remedy

Pass a Hermitian matrix as an input parameter to Decompose.

See Also

• Function calls and parameters
• User-Defined Functions
• Matrix functions
• Hermitian matrices
• Cholesky decomposition
• Decompose
• Complex Numbers
• Transpose
• RealPart
• ImPart
• Gaussian