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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 35,953
Recently I've stumbled upon number theory and decided to order a book which is coming soon so in the mean time I've...
Aug11-09 06:55 PM
4 2,164
Suppose V is a vector space over a field F that has multiplicative identity 1. Do we have to take, as an axiom, that...
Aug11-09 10:12 AM
9 1,466
Why is it that positive operators need to be self adjoint? Suppose T maps v from R^3 to R^2. So now <Tv, w>=<v, T*w>....
Aug11-09 09:19 AM
0 639
Does anyone know if its possible to check whether a number is a perfect square in 2 different bases ? ( I dont mean...
Aug11-09 07:48 AM
5 2,333
Hi, I'm currently reading a book on particle physics, which tells me this about SU(3): "...The generators may be...
Aug10-09 11:25 PM
6 1,211
I am an italian undergraduate maths student. I have recently written two brief mathematical papers on prime numbers....
Aug10-09 04:18 PM
3 2,223
I am reading "Linear Algebra" by Strang. In the first lesson, he talks about how to solve equations with 2 unknowns...
Aug10-09 04:11 PM
4 1,044
for all fermat no.s, fi-1=i-1-1]2 all fermat no.s are of form 6Ni+5 Ni+1=6Ni2+8Ni+2 a no. of form 6N+5 is composite...
Aug10-09 01:55 PM
27 3,723
I just started teaching myself a little bit about Hilbert spaces and functional analysis in general, and I had an idea...
Aug10-09 09:29 AM
1 2,257
\sum_{n=1}^{\infty}(-1)^{n}e^{-ln^{2}(nx)} Where x is pure-real and 0<x<infinity. I would be incredibly grateful...
Aug9-09 03:16 PM
0 1,075
Hello. I have to prove the fallowing theorem: "There is at least one prime number between n and n! (n factorial)...
Aug9-09 12:27 PM
8 3,141
given the function (or distribution) \sum_{n=0}^{\infty} f(E_n,u )= Z(u) for 'f' an arbitrary function and E_n ...
Aug7-09 04:26 PM
1 1,422
Hi, I wonder if there is some agreed-upon best way to reconstruct the matrix of a positive definite operator A using...
Aug7-09 03:16 PM
0 557
I came across this Proposition in my book, and I know it's something really simple that I'm missing, but I can't seem...
Aug7-09 08:51 AM
1 1,467
How do i get the point of intersection of a line and a circle.. I got lots of information on this topic, but my...
Aug7-09 07:26 AM
3 10,178
Okay, so I expanded the brackets and simplified the equation from (x+4)(x-4)(x-4) to equal x3-4x2-16x+64 and I...
Aug7-09 12:59 AM
8 1,214
Does anyone know how to classify the finite-dimensional irreducible representations of so(4,C)? Can they all be built...
Aug6-09 05:08 PM
2 2,879
All matrices A\in\mathbb{C}^{n\times n} have at least one eigenvector z\in\mathbb{C}^n. I'm interested to know what...
Aug6-09 07:06 AM
4 2,916
Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?
Aug5-09 09:06 PM
1 763
Can every real number be written as a sum of 2 real squares, and if not, how to prove that? And how to prove that not...
Aug4-09 10:47 PM
14 2,390
Hi There I'm working on Lanczos type algorithms and trying to develop some new versions of Lanczos algorithm...
Aug4-09 06:35 PM
0 970
I've been going through properties of determinants of matrices and found the following: Assuming products are...
Aug4-09 02:43 PM
3 3,531
Suppose U is a finite-dimensional real vector space and T ∈ L(U). Prove that U has a basis consisting of eigenvectors...
Aug4-09 01:33 PM
8 1,440
The couple of proofs that I've seen of Schwarz's inequality \left|\mathbf{u} \cdot \mathbf{v} \right| \leq...
Aug4-09 09:38 AM
6 3,432
I've read a number of tutorials on Clifford algebra, but I am still unsure of some elementary concepts. For...
Aug4-09 08:32 AM
4 1,780
Statement: One of the key elements in being in what people call group is that elements must be associative. So...
Aug1-09 03:51 PM
1 1,217
In the appendix B of Goldstein's classical mechanics (3rd edition), the authors discussed the dihedral group and said:...
Jul31-09 07:07 AM
0 1,239
If Q is an m x n (m > n) matrix with orthonormal columns, we know that Q^TQ = I of dimension n x n. I have a question...
Jul29-09 05:55 PM
5 3,074
Kind of a random question, but it came up in an online discussion I was having recently about a supposed proof that...
Jul29-09 04:32 PM
4 3,787
Without Sylow's theorems!! This was a problem at the end of a chapter on Lagrange's theorem. I know that every...
Jul28-09 02:42 PM
8 4,647
I recall reading somewhere that Legendre's conjecture implies the Riemann Hypothesis. But the Wiki article suggests...
Jul27-09 11:58 PM
6 1,593
This subject came up in some notes on linear algebra I'm reading and I don't get it. Please help me understand. --...
Jul27-09 11:36 PM
7 1,140
I've been stuck on this for a while now, and I was wondering if anyone could help me out. The problem is: If...
Jul27-09 11:35 AM
16 3,171
Given positive integers a, b, c, d and for fractions a/b and c/d, it seems that ( a + c )/( b + d ) is between...
Jul27-09 11:18 AM
1 2,345
I am looking for two rotation matrices M1 and M2, which describe a rotation by an arbitrary angle around the axes...
Jul26-09 05:30 AM
4 1,441
A set of vectors V defines a Euclidean subspace. A subspace contains the zero vector. Now consider augmenting this...
Jul26-09 05:27 AM
2 824
Hi I have this question for my Linear Algebra class and I can't seem to figure it out. Let A and B be n x n...
Jul26-09 05:21 AM
2 4,492
Dear all, I have a question concerning Faugere's improved F4 algorithm. You can find it in the attached file ...
Jul25-09 11:56 AM
6 2,919
I've been trying to work out a bunch of problems that have to do with finding irreducible polynomials, and this one...
Jul25-09 09:25 AM
1 2,040
Hello. I wasn't sure whether to post this here on in some of the physics sections. I have a rank 2 tensor in one...
Jul25-09 08:12 AM
2 1,026

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