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Hermitian Part

Every complex matrix can be broken into a Hermitian part

A_H=1/2(A+A^H)

(i.e., A_H is a Hermitian matrix) and an antihermitian part

A_(AH)=1/2(A-A^H)

(i.e., A_(AH) is an antihermitian matrix). Here, A^H denotes the adjoint.

See also

Antihermitian Matrix, Antihermitian Part, Antisymmetric Matrix, Antisymmetric Part, Conjugate Transpose, Hermitian Matrix, Symmetric Matrix, Symmetric Part

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Cite this as:

Weisstein, Eric W. "Hermitian Part." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HermitianPart.html

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