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hermitianmatrix

hermitian matrix

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There are 15 letters in HERMITIANMATRIX ( A¹E¹H⁴I¹M³N¹R¹T¹X⁸ )

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Definitions of hermitian matrix in various dictionaries:

HERMITIAN MATRIX - In mathematics, a Hermitian matrix (or self- adj oint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the el...

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Hermitian matrix might refer to
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:* or in matrix form: * * * * * A * * Hermitian * * * * ⟺ * * * A * = * * * * A * * * T * * * * ¯ * * * * * {\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 * * * * A * * * {\displaystyle A} * is denoted by * * * * * A * * * H * * * * * * {\displaystyle A^{\mathsf {H}}} * , then the Hermitian property can be written concisely as * * Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are * * * * * A * * * H * * * * = * * A * * † * * * = * * A * * ∗ * * * * * {\displaystyle A^{\mathsf {H}}=A^{\dagger }=A^{\ast }} * , although note that in quantum mechanics, * * * * * A * * ∗ * * * * * {\displaystyle A^{\ast }} * typically means the complex conjugate only, and not the conjugate transpose. * *

Hermitian matrix might refer to

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:* or in matrix form:
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* {\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
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* {\displaystyle A^{\mathsf {H}}}
* , then the Hermitian property can be written concisely as
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* Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are
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* {\displaystyle A^{\mathsf {H}}=A^{\dagger }=A^{\ast }}
* , although note that in quantum mechanics,
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* ∗
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* {\displaystyle A^{\ast }}
* typically means the complex conjugate only, and not the conjugate transpose.
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hermitianmatrix