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 …

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 …

This question is homework from Scott Aaronson's 2017 Quantum Information course. a) Give an example of a 2x2 unitary matrix where the diagonal entries are 0 but the off-diagonal entries …

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 …

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^ …

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

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

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} …

A good reference on unitary groups in general is (as B R suggested) the book Algebraic Groups and Number theory by Platonov and Rapinchuk, especially Chapter 2 and 6. Another good …

Jan 5, 2024 · How do i prove that this matrix is unitary? Ask Question Asked 1 year, 10 months ago Modified 1 year, 10 months ago