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 - Is there a $4 \times 4$ unitary matrix with $0 ...
This question is homework from Scott Aaronson's 2017 Quantum Information course. a) Give an example of a 2x2 unitary matrix where the diagonal entries are 0 but the off-diagonal entries …
linear algebra - Why do the columns of a unitary matrix form an ...
So I'm trying to understand why the columns of a unitary matrix form an orthonormal basis. I know it has something to do with the inner product, but I don't fully understand that either (we learned...
prove that an operator is unitary - Mathematics Stack Exchange
Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 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 · A unitary matrix $U \in \mathbb C^ {n \times n}$ can always be written in exponential form $$U = e^ {iA} \tag {1}$$ where $A$ is Hermitian. My goal is to find the …
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} …
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 …
Operator - Exponential form - Mathematics Stack Exchange
May 11, 2015 · A unitary operator is a diagonalizable operator whose eigenvalues all have unit norm. If we switch into the eigenvector basis of U, we get a matrix like: \begin {bmatrix}e^ …
On certain decomposition of unitary symmetric matrices
Jul 20, 2012 · On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 3 months ago Modified 11 years, 10 months ago