What is the difference between isometric and unitary operators on …
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 …
linear algebra - Norm preservation properties of a unitary matrix ...
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} …
linear algebra - What's the interpretation of a unitary matrix ...
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 …
Given a unitary matrix $U$, how do I find $A$ such that $U=e^{iA}$?
Jan 1, 2015 · I believe the way you propose is quite standard. For a more general understanding of exponentiation, maybe look for an introductory course on Lie groups and Lie algebras, but …
linear algebra - Matrices which are both unitary and Hermitian ...
are both unitary and Hermitian (for $0 \le \theta \le 2\pi$). I call the latter type trivial, since its columns equal to plus/minus columns of the identity matrix. Do such matrices have any …
linear algebra - How do i prove that this matrix is unitary ...
Jan 5, 2024 · How do i prove that this matrix is unitary? Ask Question Asked 1 year, 11 months ago Modified 1 year, 11 months ago
linear algebra - Singular value decomposition for unitary matrices ...
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 …
If H is Hermitian, show that $e^{iH}$ is unitary
If H is Hermitian, show that eiH e i H is unitary Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago
prove that an operator is unitary - Mathematics Stack Exchange
Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago
If matrix $A$ is unitary and $B^2 = A$ then $B$ is also unitary
Mar 26, 2019 · I think the statement is true since the unitary matrix A can only be Identity matrix I or negative identity matrix $-I$; and $B=A^2$ is an identity matrix which makes sure it is unitary.