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 …
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.
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 …
linear algebra - How unique are $U$ and $V$ in the singular value ...
Jan 20, 2014 · From all this, we see that U U and V V are unique up to unitary transformations of the eigenspaces of M∗M M ∗ M and unitary transformations of (image M)⊥ (image M) ⊥.
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 …
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 …
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