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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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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
micromass
1 30,530
Hello, This is not a homework exercise, so I decided to post it here. Hopefully one of you could help. I would like...
Nov19-12 03:03 PM
micromass
1 816
For any A \in \mathcal{R}^{n \times m}, does A^T A have an inverse? From the wikipedia article for transpose (...
Nov19-12 12:09 PM
D H
5 850
hi , I met lot's of binary operation which is associative and commtative and I also met lot's of binary operation...
Nov19-12 07:10 AM
Dead Boss
5 1,061
I am curious about under what conditions the powers of a square matrix can equal the identity matrix. Suppose that...
Nov19-12 01:26 AM
Norwegian
3 1,137
In your opinion. Or feel free to quote some people on their views of the answer.
Nov18-12 07:56 PM
micromass
17 3,206
Hi! I just need a "yes" or "no" answer. If i have to show that two lie algebras are isomorphic, is it...
Nov18-12 06:54 AM
parton
2 758
I have this problem: 1. θ is 0, θ1]T and θreplicated = 0, θ0, θ1, θ1]T, further θ is a gaussian with mean mθ and...
Nov18-12 05:31 AM
quantumlight
0 590
I have created a program in javascript that has tested integers on the collatz conjecture. Recall that the collatz...
Nov17-12 12:26 PM
phillip1882
1 1,770
Hello, Would it be correct to say that if for every two different vectors x and y, A*x ≠ A*y (where A is a...
Nov16-12 03:57 PM
AlephZero
8 1,065
I'm doing my senior project about Compressed sensing, I have some problems with some algorithms. 1)Can any body help...
Nov16-12 09:14 AM
giaoduong
1 773
Hi all, I have a linear algebra question relating actually to control systems (applied differential equations) ...
Nov16-12 09:07 AM
X89codered89X
1 739
So I was working through some problems in Herstein's Algebra on my own time, and I came across something I wasn't so...
Nov15-12 11:00 PM
mathwonk
8 2,001
Let k\in\mathbb{N}, and q be a prime factor of F_{k}=2^{2^{k}}+1. Deduce that gcd(q-1,2^{k+1})=2^{k+1}. ...
Nov15-12 11:49 AM
TaliskerBA
1 1,458
I need help or direction on how to prove that if A = S^2 - (T^2 + T)/2 Then 8A-1 can not be factored into the form B*C...
Nov15-12 07:41 AM
Norwegian
4 1,787
Is there one? I know A= and A-1= So I know that A and A-1 have the same eigenvalues, I know that this is not...
Nov14-12 04:57 PM
BrainHurts
7 1,331
Hi, Algebraists: Say V is finite-dimensional over F . Is there more than one way of defining the action of F on...
Nov14-12 04:19 PM
Erland
1 759
Suppose that M and N are natural numbers, such that N>M-1. Prove that N≥M The problem above is a rather minor...
Nov14-12 09:28 AM
Vargo
6 1,634
Hey! I have a certain problem. Let M ≥ 4 be an even number and consider the set \frac{M}{2}-1]. The problem is to...
Nov13-12 12:36 PM
Constantinos
0 754
I am wondering about the relation betwen RRE forms and identity matrices. Consider the reduced row echelon form of any...
Nov13-12 10:00 AM
Erland
8 1,540
The Cantor-Schreuder-Berstien theorem states that if there exists a one-to-one function from X to Y and the reverse...
Nov13-12 02:42 AM
micromass
4 804
What is the best way of introducing determinants on a linear algebra course? I want to give real life examples of...
Nov12-12 09:31 PM
mathwonk
3 850
I am trying to understand the quantum algorithm for order finding, but I can't find the proof anywhere. Can anyone...
Nov12-12 08:18 PM
jhendren
1 1,262
So I've been reading a bit about automorphisms today and I was wondering about something. I'm particularly talking...
Nov12-12 08:12 PM
Zondrina
6 908
the polynomial x^4+8x+12=0 has the Galois group A4. I have all its roots, but can't figure out its splitting field. ...
Nov12-12 06:55 PM
Jim Kata
7 1,053
Hi, this is not a homework problem, i just have a hard time following the sequence of this In the book , it shows a...
Nov12-12 05:50 PM
mickles
4 1,427
Hi, I need help in the following demonstration: If (m,n)=d then \Phi(mn)=\frac{d}{\Phi(d)}\Phi(m)\Phi(n) ...
Nov12-12 05:04 PM
PiAreSquared
1 1,080
I'm trying to understand a process called order finding as I need to know it for Shor's algorithm in quantum...
Nov12-12 03:31 PM
Erland
2 1,556
Consider θ:Z -> Z is a mapping where θ(n) = n^3 and it's homomorphism under multiplication. In this case, it's not a...
Nov12-12 02:28 PM
Turnyface
9 814
Hello everybody I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent. My...
Nov12-12 12:08 PM
Vargo
2 989
Hi, All: Let V be a finite-dimensional space, which can be decomposed as: V=Z(+)W . How can we express the...
Nov12-12 11:53 AM
Vargo
1 707
I understand how to find an implicit description if given the span of, say, two vectors. How do I go about finding an...
Nov11-12 11:38 AM
hogrampage
4 1,049
f(x) will give us the smallest integer m such that y^m \equiv 1 \bmod{x} given that x and y are coprime how would...
Nov11-12 05:30 AM
dodo
6 2,042
I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and...
Nov10-12 07:47 PM
mathwonk
2 918
How should one prove that the integers form a commutative ring? Im not sure exactly where to go with this and how much...
Nov10-12 03:22 PM
Square1
2 846
My prof uses this all over his notes, and I'm still not 100% sure what he means by it: CB or BB From what...
Nov10-12 02:15 PM
Stephen Tashi
1 677
I was wondering if there are any theorems that specify an exact number of subgroups that a group G has, maybe given...
Nov9-12 02:42 PM
Vargo
1 840
As part of a larger problem involving classifying intertwining operators of two group representations, I came across...
Nov8-12 01:54 PM
Vargo
2 989
Ok, so I understand that a vector space is basically the span of a set of vectors (i.e.) all the possible linear...
Nov8-12 01:51 PM
Vargo
9 944
Hi, I want to whether there is a function (/matrix) such that it can generate a m-dimensional vector such that this...
Nov8-12 08:13 AM
mathwonk
1 953
Very much a beginner in maths and broadening my horizons. I have a series of polynomials that I was hoping to get some...
Nov8-12 04:11 AM
Guffel
1 1,607

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