What is the difference between isometric and unitary operators on a ...
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 …
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 value …
prove that an operator is unitary - Mathematics Stack Exchange
Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 7 months ago Modified 5 years, 7 months ago
Prove that the tensor product of unitary matrices is also unitary
Dec 6, 2020 · Show that if $A$ and $B$ are unitary matrices, then $C = A \\otimes B$ is unitary.
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 space then …
How to do a unitary diagonalization of a normal matrix?
Nov 7, 2016 · The result does not give me the diagonal matrix with the desired eigenvalues though. Also, Google search did not yield a single nicely explained way to do a unitary transform of a normal …
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} \mathbf {U}^*. \end …
Spectrum of unitary operators lie in the unit circle
Feb 13, 2018 · Spectrum of unitary operators lie in the unit circle [duplicate] Ask Question Asked 7 years, 11 months ago Modified 7 years, 11 months ago
functional analysis - Unitary conjugation between self-adjoint ...
Apr 22, 2025 · Unitary conjugation between self-adjoint operators up to commuting remainder Ask Question Asked 9 months ago Modified 9 months ago
If H is Hermitian, show that $e^ {iH}$ is unitary
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 …