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 - 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 …
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
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 - 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
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. …
How to prove that a matrix $U$ is unitary, if and only if the …
By definition a matrix $T$ is unitary if $T^*T=I.$ For two real matrices $A,B$, the $i,j$ entry of $AB$ is the inner product of the $i$ row of $A$ and $j$ column of $B$.
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, 6 months ago
linear algebra - How unique are $U$ and $V$ in the singular value ...
Jan 20, 2014 · From all this, we see that $U$ and $V$ are unique up to unitary transformations of the eigenspaces of $M^*M$ and unitary transformations of $ (\operatorname {image} M)^\perp$.
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 …