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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 35,895
hi. i have recently become very interested in the idea of the nth roots of unity. i have discovered how to calculate...
Dec5-09 09:53 PM
1 1,328
I've been sick with mono for the past month and am trying to catch up in my Algebra class, but being so far behind I'm...
Dec5-09 09:08 PM
0 657
My question is regarding abstract algebra. Suppost that B is a 10-cycle. For...
Dec5-09 12:06 PM
Huyen Nguyen
3 2,419
I'm using this formula for my quaternion camera in OpenGL. It works perfectly but I didn't understand how it was...
Dec5-09 05:20 AM
0 1,091
How do I take the cross product of Two 3x3 Matrices. For example what is cross product of: x
Dec4-09 09:09 AM
5 10,105
In short: does every vector space have a "standard" basis in the sense as it is usually defined i.e. the set...
Dec4-09 06:16 AM
4 3,090
My textbook doesn't seem to explain it clearly enough for me to comprehend. But from what I can see, after getting the...
Dec4-09 06:02 AM
2 13,465
Suppose that p and q are odd primes and p=2q+1. Suppose that α∈ Z_p^*,α≢1 mod p. Prove that α is primitive...
Dec3-09 08:03 PM
robert Ihnot
4 3,504
dear all how do you find the eigenvalues and eigenvectors of a complex matrix? 0 ; -i ; ...
Dec3-09 04:02 PM
1 4,763
Define T: F^2 --> P_1(F) by T(a, b) = a + bx (with P_1 denoting P sub 1) I usually prove problems such as this...
Dec3-09 08:10 AM
2 4,066
Hello, I wonder if somebody could point me to a book (preferably), or paper, link, etc. which explores the relations...
Dec3-09 02:01 AM
6 2,146
So I found the characteristic equation of a matrix, and I know the roots of the equation are supposed to be the...
Dec2-09 06:02 PM
1 935
Hello Lately, I have been studying some group theory. On my own, I should add, so I don't really have any professor...
Dec2-09 05:30 PM
3 902
I have a vector of all ones in n-dimensions. For example (1,1,1) in 3D. I want to find a invertible rotation matrix T...
Dec2-09 01:21 PM
8 2,000
Hi guys just a quick question on how I would go about showing the units of Z21 is isomorphic toC2*C6(cyclic groups).I...
Dec2-09 08:53 AM
5 1,035 I started by saying cince c = me mod n (1) then me ≡ c mod n Since...
Dec2-09 08:05 AM
0 943
I'm trying to follow some notes in class. so the original equation is: u= and we let x=z+1. Then by...
Dec1-09 09:47 AM
1 956
So I have a system of equations (composed of force and moment eqns) and I can split them up into matrices which will...
Dec1-09 03:30 AM
9 28,153
Hello, I am looking into proving that the Chinese Remainder Theorem will work for two pairs of congruences IFF a...
Dec1-09 02:01 AM
2 2,457
If we call <a> the "span" of a, then I need some clarification on the concept of span. def. if G is a group and...
Nov30-09 06:23 PM
1 837
Hi, I have spme questions about Fermat's little theorem- I...
Nov30-09 07:04 AM
2 1,243
Ok so i was thinking about it recently, why do we use the decimal system as opposed to other counting systems in math?...
Nov30-09 06:34 AM
18 3,315
I am having trouble getting my head around typical arguments involving natural transformations. Is there anyway...
Nov29-09 01:44 PM
0 698
H,K are normal subgroups of a (finite) group G, and K is also normal in H. If G/K and G/H are simple, does it follow...
Nov29-09 09:03 AM
6 1,202
Let me start by saying I do not have a lot of background in linear algebra, but I'm not afraid of learning. I am...
Nov29-09 07:07 AM
1 1,539
How do I find all irreducible matrix representations of group d4?
Nov29-09 07:04 AM
0 2,568
Okay, so I'm trying to finish of a problem on integral closure and I am rather unsure if the following fact is true: ...
Nov28-09 11:17 AM
5 1,197
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
4 879
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 1,297
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
2 773
I was reading "Principles of Quantum Mechanics" - Shankar, and I'm having trouble understanding the inner product. Can...
Nov24-09 09:09 PM
2 823
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 2,347
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 2,749
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 2,857
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 1,896
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
0 893
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 4,812
fin all natural numbers n that n\sigma (n) \equiv 2(mod\varphi(n))
Nov21-09 05:51 PM
5 1,473
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 1,409
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 3,570

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