Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose. That is, if the element in the ⁠ j {\displaystyle j} ⁠-th row and ⁠ k {\displaystyle k} ⁠-th column of a Hermitian matrix ⁠ A {\displaystyle A} ⁠ is some complex number ⁠ A j k = x + i y {\displaystyle A_{jk}=x+iy} ⁠, then the element in the ⁠ k {\displaystyle k} ⁠-th row and ⁠ j {\displaystyle j} ⁠-th column is its complex conjugate ⁠ A k j = A j k ¯ = x − i y {\displaystyle A_{kj}={\overline {A_{jk}}}=x-iy} ⁠, for every pair of indices ⁠ j {\displaystyle j} ⁠ and ⁠ k {\displaystyle k} ⁠.

Source: Wikipedia — Hermitian matrix (CC BY-SA 4.0)

Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose. That is, if the element in the ⁠ j {\displaystyle j} ⁠-th row and ⁠ k {\displaystyle k} ⁠-th column of a Hermitian matrix ⁠ A {\displaystyle A} ⁠ is some complex number ⁠ A j k = x + i y {\displaystyle A_{jk}=x+iy} ⁠, then the element in the ⁠ k {\displaystyle k} ⁠-th row and ⁠ j {\displaystyle j} ⁠-th column is its complex conjugate ⁠ A k j = A j k ¯ = x − i y {\displaystyle A_{kj}={\overline {A_{jk}}}=x-iy} ⁠, for every pair of indices ⁠ j {\displaystyle j} ⁠ and ⁠ k {\displaystyle k} ⁠.

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Source: Wikipedia "Hermitian matrix" · CC BY-SA 4.0

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