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# Hermitian Matrix

Aman Bansal
592 Points
9 years ago

Dear Akram,

In mathematics, an Hermitian matrix (or self-adjoint matrix) is a square matrix with complex entries 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:

$a_{i,j} = \overline{a_{j,i}}\,.$

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

Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of having eigenvalues always real.

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