All Questions
Tagged with unitary-representations matrices
8 questions
5
votes
3
answers
420
views
Parametrization of real-valued SU(N)
I want to construct a $SU(N)$ matrix $V$, with the following property:
All the elements of the first row are given, i.e. $V_{1,j}=a_i$ (with $\sum_i a_i^2=1$)
All matrix elements are real, i.e. $V_{i,...
- 155
6
votes
2
answers
313
views
Representation over matrices $A_i^3=I$, $A_0A_1^\dagger+A_1A_2^\dagger+A_2A_0^\dagger=0$, $A_0^\dagger A_1+A_1^\dagger A_2+A_2^\dagger A_0=0$
I would like to know what all the possible finite-dimensional representations of the following relations are.
$$A_0^3 = A_1^3 = A_2^3 = I \tag{1}$$
$$A_0 A_1^\dagger + A_1 A_2^\dagger + A_2 A_0^\...
- 583
1
vote
0
answers
43
views
relationships between $AA^T$ and $[(I-A)(I-A)^T]^{-1}$ with $A$ being strictly lower triangular
I have a matrix $A$ which is strictly lower triangular. Now, I am trying to find some general statements/relationships of following matrices $U,D,V,K$ defined as:
$AA^T=VKV^H$,
$[(I-A)(I-A)^T]^{-1}=...
- 21
6
votes
1
answer
627
views
A sufficient condition (or not) for positive semidefiniteness of a matrix?
Let $A\in M_{n}(\mathbb{C})$ be a Hermitian matrix. If for all $z_1,...,z_n\in\mathbb{C}$, $$\sum_{i,j=1}^{n}A_{ij}z_{i}\overline{z_{j}}\ge 0$$ then A is positive semidefinite.
I do not think the ...
- 7,057
2
votes
2
answers
535
views
Is anything known about the eigenspectrum of the regular representation of the permutation group?
I am looking for information like upper bounds on how many times any eigenvalue can occur or something like how many eigenvalues can be there in some given range. Is anything like this known?
The ...
- 1,893
3
votes
0
answers
193
views
Method to Generate Random Mutually Orthogonal Unitary Matrices
The title says it all, I'd like to know if such a method exists to generate random mutually orthogonal unitary matrices. If so, any supplementary references would be very much obliged. Thanks again!
- 133
4
votes
0
answers
1k
views
How to find the unitary matrices in this exponential matrix representation
In the following post
Representing a product of matrix exponentials as the exponential of a sum
there is a statement regarding the result of the multiplication of two matrix exponentials:
if $A$ and $...
- 149
0
votes
2
answers
1k
views
Similarity about unitary matrices
Suppose $G_1, \ldots, G_k$ are unitary, Hermitian, and anti-commuting matrices, and assume the same for $F_1, \ldots, F_k$. Suppose these matrices are similar, i.e. there exists $T \in GL_n(\mathbb{C})...
- 651