Difference between revisions of "Manuals/calci/HERMITIAN"

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*A Hermitian matrix is defined as the square matrix with complex  entries which is equal to its own conjugate transpose.  
 
*A Hermitian matrix is defined as the square matrix with complex  entries which is equal to its own conjugate transpose.  
 
*i.e., the matrix A is Hermitian if and only if <math>A=A^T</math>, where <math>A^T</math> denotes the conjugate  transpose, which is equivalent to the condition <math> a_{ij}=\bar {a^{ji}}</math>.
 
*i.e., the matrix A is Hermitian if and only if <math>A=A^T</math>, where <math>A^T</math> denotes the conjugate  transpose, which is equivalent to the condition <math> a_{ij}=\bar {a^{ji}}</math>.
*A hermetian matrix is also called as self-adjoint matrix.
+
*A hermitian matrix is also called as self-adjoint matrix.
 
*The following matrix is the example of 3x3  Hermitian matrix:
 
*The following matrix is the example of 3x3  Hermitian matrix:
 
<math>\begin{bmatrix}
 
<math>\begin{bmatrix}
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==Examples==
 
==Examples==
*1.MATRIX("hermitian")
+
*1.MATRIX("hermitian") = -72
 +
*2.MATRIX("hermitian",3)  
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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| 49 + 40i || 0 + -34i || -33  
 
| 49 + 40i || 0 + -34i || -33  
 
|}
 
|}
*2.MATRIX("hermitian",5)
+
*3.MATRIX("hermitian",5)
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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| -13 + 21i || 83 + 95i || 88 + 81i || -70 + 92i || -7
 
| -13 + 21i || 83 + 95i || 88 + 81i || -70 + 92i || -7
 
|}
 
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|dEKS8ou6F7k|280|center|Hermitian Matrix}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
 +
*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix]

Latest revision as of 02:10, 26 October 2015

MATRIX("HERMITIAN",order)


  • is the order of the Hermitian matrix.

Description

  • This function gives the Hermitian matrix of order 3.
  • A Hermitian matrix is defined as the square matrix with complex entries which is equal to its own conjugate transpose.
  • i.e., the matrix A is Hermitian if and only if , where denotes the conjugate transpose, which is equivalent to the condition .
  • A hermitian matrix is also called as self-adjoint matrix.
  • The following matrix is the example of 3x3 Hermitian matrix:

.

  • The diagonal elements must be real, as they must be their own complex conjugate.
  • An integer or real matrix is Hermitian iff it is symmetric.
  • In calci, users can change the order and number of the Hermitian matrices.

Examples

  • 1.MATRIX("hermitian") = -72
  • 2.MATRIX("hermitian",3)
-62 -48 + 4i 49 + -40i
-48 + -4i -54 0 + 34i
49 + 40i 0 + -34i -33
  • 3.MATRIX("hermitian",5)
-90 -75 + 79i 56 + -17i 92 + -51i -13 + -21i
-75 + -79i -19 -77 + -19i 42 + 47i 83 + -95i
56 + 17i -77 + 19i -60 -25 + -26i 88 + -81i
92 + 51i 42 + -47i -25 + 26i -89 -70 + -92i
-13 + 21i 83 + 95i 88 + 81i -70 + 92i -7

Related Videos

Hermitian Matrix

See Also

References