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<div style="font-size:30px">'''HERMITIAN'''</div><br/>
<div style="font-size:30px">'''MATRIX("HERMITIAN",order)'''</div><br/>
*<math>order</math> 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 A=A^T, where A^T denotes the conjugate transpose, which is equivalent to the condition a_(ij)=a^__(ji).
*A hermetian matrix is also called as self-adjoint matrix.
*The following matrix is the example of 3x3 Hermitian matrix:
<math>\begin{bmatrix}
2 & 2+i & 4 \\
2-i & 3 & i \\
4 & -i & 1 \\
\end{bmatrix}</math>.
*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")
{| class="wikitable"
|-
| -62 || -48 + 4i || 49 + -40i
|-
| -48 + -4i|| -54 || 0 + 34i
|-
| 49 + 40i || 0 + -34i || -33
|}
*2.MATRIX("hermitian",5)
{| class="wikitable"
|-
| -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
|}
==See Also==
*[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]]
*[[Manuals/calci/CONFERENCE| CONFERENCE]]
*[[Manuals/calci/CIRCULANT| CIRCULANT]]
*[[Manuals/calci/HANKEL| HANKEL]]
==References==