Difference between revisions of "Manuals/calci/HERMITIAN"

Revision as of 12:26, 24 April 2015

MATRIX("HERMITIAN",order)

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 hermetian 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.

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 *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 <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.
 *The following matrix is the example of 3x3  Hermitian matrix: