Difference between revisions of "Error Messages/41278"

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 i^th row and j^th column is equal to the complex conjugate of the entry in the j^th and i^th 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.

@@ Line 1: / Line 1: @@
-= Example Messsage =
+[[Category: Error messages]]
- Array is not Hermitian in function [[Decompose]].  A [http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian] matrix
+== 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.
+:<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>
-= See Also =
+== 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 [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.
+A Hermitian matrix, <code>A</code>, indexed by <code>I</code> and <code>J</code>, is a matrix with the following property:
+:<code>A = ComplexConjugate(Transpose(A, I, J))</code>
+Stated differently, this means that for any element:
+:<code>RealPart(A[I = m, J = n]) = RealPart(A[J = m, I = n])</code>
+:<code>ImPart(A[I = m, J = n]) = -ImPart(A[J = m, I = n])</code>
+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]]
+* [http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrices]
+* [http://en.wikipedia.org/wiki/Cholesky_decomposition Cholesky decomposition]
 * [[Decompose]]
+* [[Complex Numbers]]
+* [[Transpose]]
+* [[RealPart]]
+* [[ImPart]]
+* [[Gaussian]]