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
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 …
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.
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 …
Prove the Fourier transform is a unitary linear operator
Sep 10, 2015 · I am trying to prove that the inverse of the fourier transform is equal to its adjoint (i.e. it is a unitary linear operator). I am working with the inner product $\langle s_1,s_2 \rangle=\int_ {-\...
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 …
On certain decomposition of unitary symmetric matrices
Jul 20, 2012 · On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 7 months ago Modified 12 years, 1 month ago
Does $U^* U=UU^*=I$ imply that $U$ is bounded (and thus unitary)?
Aug 29, 2024 · Wikipedia defines a unitary operator as " a bounded linear operator U: H → H on a Hilbert space H such that U ∗ U = UU ∗ = I, where U ∗ is the adjoint of U, and I: H → H is the identity …