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 …

2020年6月21日 · prove that an operator is unitary Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago

2021年1月13日 · 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 …

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} …

2015年5月11日 · 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^ …

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 …

On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 2 months ago Modified 11 years, 9 months ago

I just can't show that a unitary matrix $U$ is unitarily diagonizable. I know I need to show that $U$ is unitarily similar to a diagonal matrix, and this result is presumably a consequence of the …

2024年4月2日 · I would like to do two things: (i) confirm that I am interpreting these definitions of a unitary matrix and a unitary operator correctly and (ii) understand how to check that an …

2017年12月8日 · @TobiasKildetoft The unitary group (and finite groups/fields in general) come up quite often in geometric settings, as the finite classical groups act naturally on projective …