A stronger notion is unitary equivalence, i.e., similarity induced by a unitary transformation (since these are the isometric isomorphisms of Hilbert space), which again cannot happen between a nonunitary …

Definition (Unitary matrix). A unitary matrix is a square matrix $\mathbf {U} \in \mathbb {K}^ {n \times n}$ such that \begin {equation} \mathbf {U}^* \mathbf {U} = \mathbf {I} = \mathbf {U} \mathbf {U}^*. \end …

May 11, 2015 · A unitary operator is a diagonalizable operator whose eigenvalues all have unit norm. If we switch into the eigenvector basis of U, we get a matrix like: \begin {bmatrix}e^ {ia}&0&0\\0&e^ …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago

Jan 13, 2021 · I know the title is strange, but there are many instances in quantum information in which one is interested not in diagonalizing a unitary matrix, but instead in finding its singular value …

So I'm trying to understand why the columns of a unitary matrix form an orthonormal basis. I know it has something to do with the inner product, but I don't fully understand that either (we learned...

Unitary matrices are the complex versions, and they are the matrix representations of linear maps on complex vector spaces that preserve "complex distances". If you have a complex vector space then …

In the case where H is acting on a finite dimensional vector space, you can essentially view it as a matrix, in which case (by for example the BCH formula) the relation you state in a) is valid. More …

Jul 20, 2012 · On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 4 months ago Modified 11 years, 11 months ago

May 2, 2022 · $A$ and $B$ are simultaneously diagonalizable: there is a unitary matrix $U$ such that both $U^*AU$ and $U^*BU$ are diagonal. How can I prove the above statements?