Question

prove of hermition matrix​

Answer 1

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■》 In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:

{\displaystyle A{\text{ Hermitian}}\quad \iff \quad a_{ij}={\overline {a}}_{ji}}

or in matrix form:

{\displaystyle A{\text{ Hermitian}}\quad \iff \quad A={\overline {A^{\mathsf {T}}}}.}

Hermitian matrices can be understood as the complex extension of real symmetric matrices.

If the conjugate transpose of a matrix {\displaystyle A} is denoted by {\displaystyle A^{\mathsf {H}}}, then the Hermitian property can be written concisely as

{\displaystyle A{\text{ Hermitian}}\quad \iff \quad A=A^{\mathsf {H}}}

Answer 2

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