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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 35,147
\frac{0}{0} Is it 0 or undefined? I thought this was interesting, it seems a paradox in its own.
Mar31-12 11:25 AM
65 12,231
If A = {(x,y) : x = y = e, yx = xˉy} and B = {(u,v) : u^4 = v = e, vu = uˉv}, how do I go about finding the...
Mar28-12 12:02 AM
1 2,234
true or false .. The system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R) is not a field under matrix addition (+)...
Mar28-12 07:39 AM
1 739
I asked this question on one another forum but didn't get any answer . Consider the following array of natural...
Mar27-12 11:02 AM
7 2,369
Given n by n matrices A, B, C. I know how to solve the Sylvester equation AX + XB + C = 0 using the matlab...
Mar26-12 03:24 AM
3 1,574
hello :) I was trying to prove the following result : for a linear mapping L: V --> W dimension of a domain V =...
Mar27-12 06:29 AM
5 1,179
Hi, All: I have been tutoring linear algebra, and my student does not seem to be able to understand a...
Mar25-12 09:51 PM
5 1,062
I'm completely lost on this one. I need this to be able to solve that the square root of three is irrational. So it's...
Mar26-12 04:55 PM
4 1,928
Hello, it's been a while since i did linear algebra. i need some help. I have this matrix: 1 1 0 0 1 0 0 0...
Mar25-12 08:34 PM
1 1,512
Would like to see a proof for the following question. Let p be a prime number. Define a set interesting if it has...
Mar29-12 07:59 AM
5 1,951
Hi Everyone, I am kind of looking some online text to understand Lie Algebra, Group Theory and so forth. I usually...
Mar27-12 08:39 PM
9 1,717
Suppose a (n x 3) matrix B is given, n>3. Also, suppose a matrix (3 x 3) matrix C is given, whose columns correspond...
Mar26-12 02:58 AM
1 984
I'm reading some notes concerning Sylow subgroups of S4: Since #S4 = 24 = 3 . 2^3 from Sylow's Theorems we know...
Mar29-12 05:50 AM
2 1,431
How the hell do you prove that the components of a vector w.r.t. a given basis are unique? I have literally no idea...
Mar26-12 01:38 PM
3 906
While studying groups, Is there a common pattern/arrangement of the group elements represented in a table? Is...
Mar27-12 03:55 PM
Number Nine
9 939
Hi all, I need to find the λ and the ai that solves the Generalized eigenvalue problem {a}=-λ2 {a} with =
Mar28-12 06:39 PM
2 1,739
Well, I have solved this problem from a textbook: Prove the Schwarz inequality. When you try to solve it, you...
Mar27-12 05:50 AM
1 754
This seems a simple question but I can't find the solution by myself. Please help. Say we have a 2 by 2 matrix with...
Mar27-12 06:06 AM
2 2,780
Well, first of all I'm not quite sure If I'm posting my question in the right section so forgive me if it's in the...
Mar30-12 11:47 AM
6 1,070
He starts using the term 'reducible', as it came out of nowhere, from the page 162 of the text. I know, roughly,...
Mar27-12 04:49 PM
2 815
In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we...
Mar28-12 08:28 PM
1 1,097
I intend to use the Gershgorin Circle Theorem for estimating the eigenvalues of a real symmetric (n x n) matrix....
Mar28-12 02:48 AM
0 1,043
i am having trouble with some hw problems in my linear algebra course... the book is brescher and the teacher is sort...
Mar28-12 10:41 AM
3 2,431
I am reading Kane - Reflection Groups and Invariant Theory and need help with two of the properties of reflections...
Mar28-12 08:19 PM
1 927
Find the dimension of the subspace of M2;2 consisting of all 2 by 2 matrices whose diagonal entries are zero. ? i...
Mar31-12 08:21 PM
8 1,396
B&F have the following: \delta_{i j} = e'_i \cdot e'_j = a_{i k} \left( e_k \cdot e'_j \right) = a_{i k} a_{j k} ...
Mar29-12 03:18 AM
2 1,115
In Dummit and Foote, a short exact sequence of R-modules 0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0...
Mar29-12 02:14 PM
2 1,238
There seem to be two definitions for a regular representation of a group, with respect to a field k. In particular,...
Mar29-12 08:11 PM
2 1,025
I am reading Kane's book on Reflections and Reflection Groups and am having difficulties with some basic geometric...
Mar30-12 06:21 PM
Math Amateur
3 887
it is possible to evaluate sums over the set of Rational so \sum_{q} f(q) with q= \frac{m}{n} and m and n are...
Mar31-12 06:39 PM
A. Bahat
4 1,724
Lets say you want to quickly pick points in order to nail some wood together to build a wooden ship. You can use...
Mar30-12 07:07 PM
1 854
Hi guys, Basically I'm playing around with modules at the moment, and I can't work out why we cant have the group...
Mar30-12 04:34 PM
6 1,106
To show that a non-abelian group G, has elements x,y,z such that xy = yz where y≠z, Is it enough to simply state...
Mar31-12 09:13 AM
5 1,085
Hey, I'm just trying to grasp ordering of groups and subgroups a little better, I get the basics of finding the...
Mar31-12 12:59 PM
3 1,473
Let's say you have four points that define a rectangle in the xy plane centered at the origin (with the x,y axes...
Mar31-12 10:34 PM
2 1,197
This has been bugging me for a while. I'm pretty sure I'm correct but I'd just like to verify to put my mind at ease....
Apr1-12 09:39 PM
2 967
Hello. A matrix has 5 columns. One of the columns is all zeros. Two of the columns have leading ones. ...
Apr1-12 09:01 PM
1 1,142
Let G be a finite group, H and K subgroups of G such that G=HK. Show that there exists a p-Sylow subgroup P of G such...
Apr1-12 09:45 PM
2 1,120
So the book asks me to sketch out these graphs, and of course there are no examples. I was wondering how this is done....
Apr2-12 04:10 AM
6 1,880
Is there a good reference on how to construct Cayley's graph of a group given a table/defining equations, and vice...
Apr2-12 10:28 AM
0 779

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