Find a unitary matrix given eigenvectors and eigenvalues
Apr 23, 2021 · Find a unitary matrix given eigenvectors and eigenvalues Ask Question Asked 4 years, 7 months ago Modified 4 years, 7 months ago
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} …
prove that an operator is unitary - Mathematics Stack Exchange
Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 6 months ago Modified 5 years, 5 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 …
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 …
Definition Unitary Group - Mathematics Stack Exchange
Dec 8, 2017 · @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 …
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 - Show that $U$ is a unitary operator if and only if ...
Apr 23, 2018 · What you show is that any unitary transformation of a unitary matrix is a unitary matrix. What is asked is to prove an operator is unitary given that its representation 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. …