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 …

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} …

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 …

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. …

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 …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago

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^ …

Dec 18, 2015 · Given that the two matrices are symmetric, it may very well be faster to separately diagonalize them first, then adjust the diagonlizing unitary matrices so that they match.

Oct 31, 2017 · I'm trying to prove the following statement: if A and B are unitarily equivalent, then they have the same singular values so my proof goes like this: unitarily ...

Jul 20, 2012 · On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 3 months ago Modified 11 years, 10 months ago