Questions tagged [unitary-matrices]
This tag is for questions relating to Unitary Matrices which are comprise a class of matrices that have the remarkable properties that as transformations they preserve length, and preserve the angle between vectors.
547 questions
- Bountied 0
- Unanswered
- Frequent
- Score
- Trending
- Week
- Month
- Unanswered (my tags)
1
vote
0
answers
100
views
Unitary representations of non-compact Lie Groups
I have often read the following statement:
Let $G$ be a connected, simple, non-compact Lie Group of dimension $n \geq 2$. Let $ρ: G \to U(H)$ be a unitary representation of $G$ on the Hilbert Space $H$...
0
votes
0
answers
60
views
Products of commuting reducible matrices
The following question arose while attempting to construct a counterexample to a previous question.
A matrix $A$ is said to be unitarily reducible if there exists a unitary matrix $U$ such that $U^tAU$...
1
vote
1
answer
264
views
Show that an integral of Chebyshev polynomial yields a Bessel function
I have an integral to solve which arises from solving a quantum eigenvalue problem for a special unitary matrix raised to an $n$-th power.
The integral is
$$\frac1{\pi}\int_0^{\pi} \cos(2n \alpha) d\...
3
votes
1
answer
131
views
For an antiunitary operator, is inverse equal to its Hermitian adjoint (i.e., $\widehat{U}^{-1} = \widehat{U}^\dagger$)?
Context
I am studying Wigner's theorem [1]. I am familiar with unitary operators. I know that for an unitary operator $\widehat{U},ドル its inverse equal to its Hermitian adjoint. In other words for a ...
6
votes
0
answers
107
views
Algorithm to determine if $A = B^k$ for any $k\geq 0$ if $A, B$ are special unitary matrices
I am working with the Lawrence-Krammer representation of $B_n$ and need to find a way to determine if, given any two matrices $A, B$ in the image of the representation, there exists $k\in\mathbb{Z}^+$ ...
10
votes
0
answers
197
views
Is there a standard algorithm to recover a representation of $U(n)$ from its character?
I am interested in computing explicitly representations of the unitary group $U(n),ドル which means that given a character in $n$ variables $\chi = \sum_{\lambda \in \mathbb{Y}, l(\lambda) \leq n} a_\...
1
vote
0
answers
60
views
Can the unitary transformation of one of the matrix preserve the invertibility of Hadamard product? [closed]
Let $A=[a_{ij}],B=[b_{ij}]\in \mathcal{M}_{n}(\mathbb{R})$ be two invertible matrices and additionally, their Hadamard product $A\odot B$ is also invertible. Consider the basic circulant permutation ...
0
votes
1
answer
47
views
Non-uniqueness of the unitary transformation
The following question has arisen in the course of a physics problem. Suppose I have two Hermitian matrices, denoted by $A$ and $B$. In the problem, I have found two distinct unitary matrices $U_1$ ...