All Questions

Suppose we have a finite square n x n matrix of complex numbers H that is Hermitian and skew-symmetric: $H^\dagger = H$ and $H^T = -H$. (T denotes transpose, $\dagger$ denote conjugate transpose. I ...

Let $\mathbf H$ be an infinite dimensional Hilbert space. I want to find an example of a $2\times 2$ real symmetric positive definite matrix $M$ and a positive definite bounded operator $A : \mathbf H ...

Let $M$ be a $3\times 3$ real invertible diagonal matrix and $H$ a Hilbert space of infinite dimension (for example, we can take $H$ as the space of square integrable functions over a bounded ...