# Manuals/calci/HERMITIAN

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**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 |