# Manuals/calci/HERMITIAN

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

Hermitian Matrix