Difference between revisions of "Error Messages/41278"

 
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= Example Messsage =
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[[Category: Error messages]]
  
Array is not Hermitian in function [[Decompose]].  A [http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian] matrix
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== Example messsage ==
is one that is equal to its own conjugate transpose, i.e., the element
 
in the i<sup>th</sup> row and j<sup>th</sup> column is equal to the complex conjugate of
 
the entry in the j<sup>th</sup> and i<sup>th</sup> 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.
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:<code>Array is not Hermitian in function Decompose.  A Hermitian matrix is one that is equal to its own conjugate transpose, i.e.,</code> :<code> the element in the i<sup>th</sup> row and j<sup>th</sup> column is equal to the complex conjugate of the entry in the j<sup>th</sup> and i<sup>th</sup> column.</code>
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== Cause ==
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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 [http://en.wikipedia.org/wiki/Hermitian_matrix 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 [http://en.wikipedia.org/wiki/Cholesky_decomposition Cholesky decomposition] of a matrix can only be obtained for a Hermitian matrix.
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A Hermitian matrix, <code>A</code>, indexed by <code>I</code> and <code>J</code>, is a matrix with the following property:
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:<code>A = ComplexConjugate(Transpose(A, I, J))</code>
  
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:
 
Stated differently, this means that for any element:
[[RealPart]](A[I=m,J=n]) = RealPart(A[J=m,I=n])
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:<code>RealPart(A[I = m, J = n]) = RealPart(A[J = m, I = n])</code>
[[ImPart]](A[I=m,J=n]) = -ImPart(A[J=m,I=n])
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:<code>ImPart(A[I = m, J = n]) = -ImPart(A[J = m, I = n])</code>
  
 
The diagonal elements are all real numbers.
 
The diagonal elements are all real numbers.
  
= See Also =
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==Remedy==
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Pass a Hermitian matrix as an input parameter to [[Decompose]].
  
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== See Also ==
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* [[Function calls and parameters]]
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* [[User-Defined Functions]]
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* [[Matrix functions]]
 
* [http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrices]
 
* [http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrices]
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* [http://en.wikipedia.org/wiki/Cholesky_decomposition Cholesky decomposition]
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* [[Decompose]]
 
* [[Complex Numbers]]
 
* [[Complex Numbers]]
 
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* [[Transpose]]
= See Also =
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* [[RealPart]]
 
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* [[ImPart]]
* [[Decompose]]
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* [[Gaussian]]

Latest revision as of 18:34, 20 April 2016


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

Comments


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