Hermitian matrices are square matrices that are equal to their own conjugate transpose. This means that for a matrix \( A \), it is Hermitian if \( A = A^* \), where \( A^* \) represents the conjugate transpose of \( A \). They have real eigenvalues and orthogonal eigenvectors, making them essential in various computational algorithms, particularly in the context of optimizing eigenvalue problems using methods like the Lanczos and Arnoldi algorithms.
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