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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 35,094
Hi! This might be a silly question, but I can't seem to figure it out and have not found any remarks on it in the...
Nov27-09 05:10 AM
4 875
Given: G is the group of matrices of the form: 1 n 0 1 Where n is an element of Z, and G is a group under...
Nov26-09 10:54 PM
3 1,276
Hello, I have an infinite monoid A and a submonoid K. let's assume I pick up an element x\in A-K, now I consider...
Nov26-09 05:24 PM
2 764
I was reading "Principles of Quantum Mechanics" - Shankar, and I'm having trouble understanding the inner product. Can...
Nov24-09 09:09 PM
2 815
Is there a name for product of the unique prime factors of a number? For example, for the number 12, it would be...
Nov24-09 03:01 PM
1 2,329
If H is a nxn primitive, irreducible matrix, is it always true that Hn-1 > 0? That is, every entry in Hn-1 is...
Nov24-09 12:51 PM
Doom of Doom
1 2,736
Does anyone know how to approach this problem? Let A be an mn matrix of rank m, where m<n. Pick a point x in R^n,...
Nov23-09 09:58 PM
6 2,834
First, remember that the OP is new to pure number theory. We all know that not every number that follows the...
Nov23-09 06:39 PM
robert Ihnot
5 1,888
Figured it would be a quick review of ideas that turned into a nightmare... x \equiv i (mod 1 + i) x \equiv 1...
Nov23-09 03:36 PM
0 886
I read this in a book (it was stats and about poisson approx to normal) Given was this: n(n-1)(n-2) \cdots (n-r+1)...
Nov23-09 10:42 AM
2 4,794
fin all natural numbers n that n\sigma (n) \equiv 2(mod\varphi(n))
Nov21-09 05:51 PM
5 1,467
There is something I don't understand about the recent concept of a "number derivative". It seems to me that the (very...
Nov21-09 06:01 AM
0 1,402
If C = A +B where A,B are both p.d, than C is p.d and its eigenvalues are positive. Waht can you say about the...
Nov20-09 02:16 PM
2 3,544
what is it?
Nov20-09 12:46 PM
2 1,664
Hey guys i am stuck with the gaus jordan method of the following matrix. A = 1 2 3 4 5 6 3 1 -2 For the co...
Nov20-09 05:56 AM
1 1,888
Here is an interesting problem I came up with during my research. I first present a slightly simplified version. Let...
Nov20-09 03:53 AM
1 1,639
Hi all, I've been staring at this question on and off for about a month: Suppose that p is an odd prime, and g...
Nov19-09 07:34 PM
4 2,944
For those of you with "A First Course in Abstract Algebra 7th ed.," I'm on chapter 15 and in particular, the first 12...
Nov19-09 06:01 PM
3 1,891
Construct a sequence that visits the numbers 0,1,5 infinitely often.? A sequence Sn visits a number A when for...
Nov19-09 12:46 PM
9 1,502
Hello, I am quite new to Geometric Algebra, this is the reason for the silly question. In Geometric Algebra, the...
Nov19-09 04:24 AM
1 910
Hi All, Is there a module such that the torsion elements do not form a submodule? Do they always form a submodule?...
Nov18-09 06:08 PM
0 828
Assuming A is a 2x2 matrix how many different matricies exist such that A^2=I ? I am 99% sure the answer is 4 but...
Nov18-09 04:16 PM
4 1,158
my idea is, if we consider the geometry of primes could we conclude they form a fractal ? , for example if we...
Nov18-09 09:21 AM
4 5,114
Proposition. A polynomial of degree 2 or 3 over a field F is reducible iff it has a root in F. Tell me if I'm on...
Nov18-09 05:51 AM
1 747
Hi! I am working on the following problem: If a matrix is antisymmetric (thus A^T = -A), show that P = {A...
Nov17-09 04:08 PM
6 1,257
think i have discovered an integral equation for the Xi-function \Xi (z)= A\int_{-\infty}^{\infty} \phi...
Nov17-09 09:19 AM
1 1,720
Hay all, I am stuck on a problem, and its driving me crazy. I have a problem, xN = a mod b. Where I have to solve for...
Nov17-09 07:48 AM
5 1,884
So I just bought his ook called "Matrices and Linear Algebra" by Hans Schneider and G.P. Barker in an attempt to teach...
Nov17-09 06:35 AM
14 3,454
Hi, I'm a grad student in pure math and I'm trying to re-learn my linear algebra from scratch because I never learned...
Nov17-09 06:25 AM
7 10,120
Let me start off by saying I have not yet had a formal course in Number Thoery and have only read briefly on the...
Nov16-09 07:33 PM
3 2,194
If I have n runners on a circular tracks at different speeds s_i, will they always meet up arbitrarily close together...
Nov16-09 11:34 AM
9 1,710
hey, how can ı show the reflections over the line do not have group structure? --reflection of the real plane...
Nov16-09 10:54 AM
1 886
how to find number (3-i)^{12} ? i know theorem for powers of complex numbers, but i have to know argument of...
Nov16-09 08:34 AM
1 1,335
Let V be a finite dimensional complex inner product space with inner product < , >. Let U be unitary with respect to...
Nov16-09 07:40 AM
4 1,960
Hi everyone, I saw that for the linear diophantine equation d=ax+by, where d=(a,b), that x and y must be coprime. ...
Nov14-09 08:10 PM
2 2,106
We have three orthonormal vectors \vec i_1 , \vec i_2, \vec i_3 , and we know wich are the components of an...
Nov14-09 03:18 PM
3 1,473
(1+2+....n)^{2} = 1^{3}+2^{3}+...n^{3} \frac{n^{2}(n+1)}{4}^{2} = 1^{3}+2^{3}+...n^{3} how do you simplify the...
Nov14-09 02:42 PM
7 5,336
Is the derivative operator d/dx bounded with respect to the norm <f,g> defined by integral from 0 to 1 of f g*...
Nov14-09 01:01 PM
2 1,291
hi can someone tell to correctly use the 10 axioms.. for example: does the set of all 3x3 symmetric matrices...
Nov14-09 04:11 AM
3 2,575
I'm going to be doing research next semester on a topic of almost entirely my choice. I'd like to research anything...
Nov13-09 03:07 PM
3 1,654

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