1/22/2024 0 Comments Hermitian adjoint of a matrixA Hermitian matrix can be expressed as the sum of a real symmetric matrix plus an imaginary skew-symmetric matrix.Every real symmetric matrix is also Hermitian.And this type of matrices always have an orthonormal basis of made up of eigenvectors of the matrix. A Hermitian matrix has orthogonal eigenvectors for different eigenvalues. This property was discovered by Charles Hermite, and for this reason he was honored by calling this very special matrix Hermitian. Therefore, the eigenvalues of a Hermitian matrix are always real numbers.Also, the obtained diagonal matrix only contains real elements. Any Hermitian matrix is diagonalizable by a unitary matrix.Although not all normal matrices are hermitian matrices. Every Hermitian matrix is a normal matrix.Hermitian matrices have the following characteristics: All of these matrices are Hermitian because the conjugate transpose of each matrix is equal to each matrix itself.
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