Hermitian Matrix
akram qashou , 14 Years ago
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Engineering Entrance Exams> Hermitian Matrix...
2 AnswersKomal
In mathematics, aHermitian matrix(orself-adjoint matrix) is asquare matrixwithcomplexentries that is equal to its ownconjugate transpose—that is, the element in thei-th row andj-th column is equal to thecomplex conjugateof the element in thej-th row andi-th column, for all indicesiandj:
[a_{ij} = \overline{a_{ji}}] or [A = \overline {A^\text{T}}] , in matrix form.
Hermitian matrices can be understood as the complex extension of realsymmetric matrices.
If the conjugate transpose of a matrix [A] is denoted by [A^\dagger] , then the Hermitian property can be written concisely as
[A = A^\dagger.]
Hermitian matrices are named afterCharles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having realeigenvalues.
[a_{ij} = \overline{a_{ji}}] or [A = \overline {A^\text{T}}] , in matrix form.
Hermitian matrices can be understood as the complex extension of realsymmetric matrices.
If the conjugate transpose of a matrix [A] is denoted by [A^\dagger] , then the Hermitian property can be written concisely as
[A = A^\dagger.]
Hermitian matrices are named afterCharles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having realeigenvalues.
sajid
In mathematics, aHermitian matrix(orself-adjoint matrix) is asquare matrixwithcomplexentries that is equal to its ownconjugate transpose—that is, the element in thei-th row andj-th column is equal to thecomplex conjugateof the element in thej-th row andi-th columnHermitian matrices are named afterCharles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having realeigenvalues
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