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-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 (...
dsimcha's user avatar
  • 159
-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 ...
Wuu tang clan's user avatar
-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 ...
SPDR's user avatar
  • 103
-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| ...
aldous99's user avatar
-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
nayreel's user avatar
-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 $A < 2 (n - 1).$
L S B. user255259's user avatar
-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 ...
Alaya's user avatar
  • 95
-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 ...
user544899's user avatar
-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 ...
Rohit Shukla's user avatar

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