Manuals/calci/HERMITIAN

MATRIX("HERMITIAN",order)

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 $a_{ij}={\bar {a^{ji}}}$ .
A hermitian matrix is also called as self-adjoint matrix.
The following matrix is the example of 3x3 Hermitian matrix:

${\begin{bmatrix}2&2+i&4\\2-i&3&i\\4&-i&1\\\end{bmatrix}}$ .

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.