All Questions
6,260 questions
-3
votes
1
answer
2k
views
Eliminating redundant linear constraints? [closed]
I have an NxN matrix of linear constraints that is not of full rank. In other words, some of the constraints are linear combinations of other constraints. The "standard" linear algebra tools (...
-3
votes
0
answers
88
views
Quantitative formula for number of invertible square matrices over a finite field? [closed]
Let $M_n(F)$ denote the set of $n\times n$ matrices for a value $n\in \mathbb{N}$ with components in a field $F$ with finite cardinality . Let $$I=\{A\in M_n(F):~~ \det(A) \neq 0 \}.$$ What is the ...
-3
votes
0
answers
162
views
A presentation for the group $GL(n,\mathbb{Z}_p)$
Let $n\ge 2$. Let $p$ be a prime and $\mathbb{Z}_p$ denote the finite field with $p$ elements.
I want to know about the presentation for the group $GL(n,\mathbb{Z}_p)$ consisting of its generators and ...
-3
votes
1
answer
134
views
SU(2) and entangled particles [closed]
We have two particles $A$ and $B$ in a maximally entangled state $|\Psi\rangle \in \cal{H}_A \times \cal{H}_B$
$$
\left|\Psi\right\rangle = \frac{1}{\sqrt{2}} ( \left| 0
\right\rangle_A\otimes \left| ...
-4
votes
2
answers
6k
views
Factorizing polynomials of several variables (in a different perespective)
I am looking for factorization of polynomials of several variables in the way outlined below.
Consider a second degree polynomial of two variables over the complex numbers.
"P(x,y) = Ax^2 + Bxy + Cy^...
-4
votes
1
answer
173
views
What are all the complex structures on $\mathbb{R}^2$ which live inside $\mathrm{SL}_2(\mathbb{Z})$? [closed]
By "complex structure" I am referring to 2x2 matrices which square to $-\mathrm{Id}_2$. I need to know those with integer entries and determinant equal to 1.
Thank you
-4
votes
1
answer
387
views
Eigenvalues of real symmetric matrix [closed]
Suppose $A$ is a $n \times n$ real symmetric matrix with entries $a_{ij}\geq 1 $ and $a_{ii} = 0 $. Is it possible to have sum of the absolute eigenvalues of
$A < 2 (n - 1).$
-4
votes
1
answer
294
views
How to calculate $y^T \mbox{diag}(A^T B A) \,y$ efficiently? [closed]
I want to calculate $$y^T \mbox{diag}(A^T B A) \,y$$ where
$y$ is a $n \times 1$ vector.
$A$ is a $m \times n$ matrix where $n \gg m$.
$B$ is a $m \times m$ symmetric positive definite matrix; the ...
-5
votes
1
answer
89
views
Why is the second order correction to energy zero for a fully degenerate eigensystem? [closed]
Consider the system given by,
$$ H|n\rangle = E|n\rangle$$
where:
$H$ is the hamiltonian.
$|n\rangle$ is the eigenstate.
$E$ is the energy of the eigenstate.
Using degenerate perturbation theory and ...
-9
votes
1
answer
338
views
Does $\|(I-A)^{-1}\|_{2} \leq 1/(1-\|A\|_{2})$ holds for matrices with spectral radius smaller then 1?
Given a symmetric positive semidefinite matrix matrix $A$, if its spectral radius $0<\rho(A)<1$, does the inequality $\|(I-A)^{-1}\|_{2} \leq 1/(1-\|A\|_{2})$ hold true?
$\|A\|_{2}$ denotes ...