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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
1 30,412
When explicitly given a set of polynomial equations, I am interested in describing its singular locus. I read this...
Feb18-12 01:23 AM
1 1,094
What is the standard for counting with composite numbers? If I can count to infinity with all odd composites and...
Feb13-12 09:35 AM
33 3,870
Hello, Background: We have a machine with two rotational axes (b,c) attached to each other. By design the B axis is...
Feb13-12 02:37 AM
7 4,258
If we assume that the Twin Prime Conjecture is true (and thus there are infinite number of primes that are 2 apart),...
Feb8-12 08:42 PM
6 2,078
hallo I am trying to calculate the probability to obtain 2 sets of linearly independent vectors from a set of...
Feb14-12 08:41 AM
5 1,654
I am trying to find nonzero prime ideals of \mathbb{Z} \oplus \mathbb {Z}, specifically those which are not also...
Feb12-12 01:03 AM
6 2,351
I know how I would be able to do this using projection, but am not so sure with dot products. Do I dot the normal...
Feb13-12 06:21 PM
3 3,411
Hi, My question is to show that the linear transformation T: M2x2(F) -> P2(F) defined by T (a b c d) = (a-d) |...
Feb9-12 03:11 PM
3 2,167
I'm confused with a question and wondered if anyone could help explain where I need to go... let x ε R. Prove that...
Feb9-12 10:36 AM
5 1,464
Well I generally haven an idea about subgroup of a group and generators. But I fail to understand following:...
Feb10-12 12:59 AM
11 1,626
I want to prove that the square of any integer is in the form of 4n or 4n + 1. I know that when we square any...
Feb10-12 04:29 PM
8 2,123
I don't understand how to show that the reflections and rotations are associative. Thanks for any help.
Feb9-12 02:08 AM
2 1,803
Ramsey Primes are those generated from a simple criteria that is easy to check. I checked all odd numbers from 1 to 1...
Feb16-12 12:55 PM
8 2,147
I'm trying to prove that every nxn matrix can be written as a linear combination of matrices in GL(n,F). I know all...
Feb9-12 02:59 PM
1 1,540
greetings . i have a couple of questions about the prime counting function . when \pi _{0}(x) changes by 1, then...
Feb9-12 11:51 AM
1 1,478
(x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + ... + x + 1) Where does this factorization come from? I need to know so I...
Feb11-12 05:26 AM
9 2,465
we have an Ipad mounted on a vehicle and would like to know that if the ipad is mounted in a tilted manner, would the...
Feb10-12 02:30 AM
1 1,149
In order to improve my knowledge of Linear Algebra I am reading Linear Algebra Done Right by Sheldon Axler. In...
Feb12-12 08:38 PM
7 1,643
Let G be a finite Group. If every proper normal subgroup of G/Z(G) is supersolvable then every proper normal subgroup...
Feb10-12 12:26 PM
0 1,086
Direct product of two irreducible representations of a finite group can be decomposed into a direct sum of irreducible...
Feb15-12 09:09 AM
5 1,851
Non-repeating patterns in decimal expansions of irrational numbers seem to have two forms. I am wondering if there is...
Feb13-12 10:07 AM
7 3,081
I was wondering if this is a correct statement, I'm assuming it is for my proof. Let e,f and g be non zero...
Feb12-12 02:14 PM
1 1,424
I'm researching a problem relatived to group SO(8). I have searched many book of theory Group but I did'n find SO(8)...
Feb13-12 02:03 AM
5 1,253
Hello Mathematician Can the matrix be differentiated with respect to a vector? Regards Aman
Feb15-12 12:46 PM
3 1,466
Why would you want to use a matrix for a linear transformation? Why not just use the given transformation instead of...
Feb18-12 11:06 AM
4 1,592
Hi guys I have a question about the coprime of two vectors For two vectors (x1,x2) and (y1,y2). Given a,b with...
Feb13-12 09:20 PM
5 1,522
I was studying (yet another) number theory problem, described here: Prove that the equation x^3+y^3+z^3+t^3=1999...
Feb17-12 02:58 PM
24 3,423
The group in question is U100, the group of units modulo 100, which, correct me if I'm wrong, is equal to {3, 7, 9,...
Feb13-12 12:40 PM
1 2,018
(1)Assume a, b and n are nonzero integers. Prove that n is divisible by ab if and only if n is divisible by a and n...
Feb15-12 02:47 PM
3 1,846
someome please help me with this problem: "Any real numbers x and y with 0 < x < y, there exist positive integers p...
Feb13-12 10:32 PM
1 1,489
Will the set of eigenvalues of an incident matrix derive an equivalent notion of a graph spectrum as it does with an...
Feb16-12 08:19 PM
1 910
If you could assume that every even number > 6 is the sum of at most 4 primes, would that help in anyway to prove it...
Feb15-12 12:53 PM
0 1,379
Feb15-12 05:37 PM
3 1,524
I'm learning about rings, fields, vector spaces and so forth. The book I have states: "Real-valued functions on...
Feb16-12 03:54 PM
10 1,799
If you consider the permutation representation of Sn in ℂ^n, i.e the transformation which takes a permutation into the...
Feb15-12 06:29 PM
2 1,147
Hi everyone, I keep seeing in textbooks and examples online that when someone proves that a set is a vector space,...
Feb16-12 01:09 AM
2 791
Letís say that we have a constant matrix A which is the coefficients matrix and column vector U of control variable as...
Feb19-12 06:16 AM
4 1,310
Hi there, I'm doing homework right now (no this isn't a homework question!) and have basic questions on...
Feb16-12 01:03 PM
3 1,596
I'm trying to prove eA eB = eA + B using the power series expansion eXt = \sum_{n=0}^{\infty}Xntn/n! and so eA eB...
Feb18-12 04:38 PM
5 2,671
Hello, i am studying vector subspacess and Axler introduces the two criteria for a vector subspace (closure under...
Feb19-12 09:38 AM
2 1,501

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