A Hermitian matrix is a matrix that is equal to its conjugate transpose. This generalizes the concept of a "symmetric matrix", since every real symmetric matrix is Hermitian. However, …

In any reasonable sense, symmetric=hermitian=self-adjoint. For genuinely unbounded operators, symmetric does not imply self-adjoint, and, unless the thing is already self-adjoint, its adjoint is …

Jun 24, 2016 · Hermitian operators (or more correctly in the infinite dimensional case, self-adjoint operators) are used not because measurements must use real numbers, but rather because …

Sep 26, 2019 · Thanks! This makes more sense, I forgot A and B were also hermitian in this problem. I appreciate the additional elaboration.

Hermitian matrices are precisely the matrices admitting a complete set of orthonormal eigenvectors such that the corresponding eigenvalues are real. So unitary Hermitian matrices …

Jul 23, 2015 · @OpenSeason Maybe quicker: any Hermitian matrix can be diagonalized. It's obvious for diagonal matrices..

Mar 25, 2017 · and this binary operation is indeed skew-symmetric, billinear and fulfills the Jacobi identity, so one can indeed, at this abstract level, define a Lie algebra of Hermitian matrices.

Apr 16, 2013 · I am trying to prove that Hermitian Matrices are diagonalizable. I have already proven that Hermitian Matrices have real roots and any two eigenvectors associated with two …

Nov 11, 2020 · Homework-like questions and check-my-work questions are considered off-topic here, particularly when asking about specific computations instead of underlying physics …

With entries strictly in $\mathbb {R}$, Hermitian matrices are just symmetric matrices so your basis is correct and is indeed the very one for symmetric matrices. However, the problem …