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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
micromass
1 35,192
Let S be a set on which a linear order <= (less or equal) , is defined. Show that a non-empty finite subset has a max.
Apr28-10 05:17 AM
Martin Rattigan
3 839
Let a,b>1 be integers such that for all n>0 we have a^n-1|b^n-1. Then b is a natural power of a. I can't find a...
Apr28-10 04:57 AM
Martin Rattigan
31 3,626
Hi, everyone. I have a question about geometric constructible numbers. I know that "if 'a' is constructible then...
Apr27-10 07:37 PM
emptyboat
2 926
for a 3 x 3 matric of values a11 a12 a13 b21 b22 b23 c31 c32 c33 the determinant will be...
Apr27-10 01:29 PM
Fredrik
1 1,918
As a generalization to some problem I've just seen, I'm wonder what the solution to the following question is: For...
Apr27-10 01:01 PM
Martin Rattigan
21 3,492
hi, i don't really understand whats the difference between vector product and dot product in matrix form. for...
Apr27-10 11:42 AM
quietrain
6 10,137
Let R be an ordered Ring. Assume R+ is well-ordered Prove: a) min(R+) = 1. b) R is an integer ring
Apr27-10 09:04 AM
g_edgar
2 775
Hello, I'm a senior mechanical engineering student. I'm trying to write an application that plots the system...
Apr27-10 04:05 AM
trambolin
14 5,230
Hi, is there any numerical invariant that would characterize the rank of a non-square matrix, similar to the...
Apr27-10 04:03 AM
trambolin
5 5,166
I need to prove the following. 1. A is a symmetric matrix, and x(transpose)*A*x=0 for all x (belongs to R^n) if and...
Apr27-10 03:55 AM
trambolin
2 1,039
(Note: this isn't a homework question, I'm reviewing and I think the textbook is wrong.) I'm working through the...
Apr26-10 05:04 PM
Dosmascerveza
8 6,022
http://img710.imageshack.us/img710/2314/booleanalgebra.jpg AFAIK logic is all about "T"/"F" or 0/1, and boolean...
Apr26-10 02:14 PM
Tac-Tics
3 1,003
I need to compute the 3 eigenvalues and 3 eigenvectors of a symmetric 3x3 matrix, namely a stress tensor,...
Apr26-10 01:05 PM
jrosen13
8 14,890
Let R be a non-commutative ring . Suppose that the number of non-units of R is finite . Can we say that R is a finite...
Apr26-10 10:54 AM
zhentil
5 1,349
Claim: If gcd(a,b,c)lcm(a,b,c) = abc, then gcd(a,b)=gcd(b,c)=gcd(a,c)=1. I'm trying to understand why this is...
Apr25-10 04:49 PM
disregardthat
6 5,116
hi guys, i have no idea of how to do the following question, could u give some ideas? Q:determine whether or not...
Apr25-10 10:59 AM
HallsofIvy
7 3,550
Let me put this here, as it's so simple that everyone can take a look at it. I must be blind not to see my...
Apr25-10 04:45 AM
ManDay
0 1,008
how do I find all u in R such that Q(u)=Q(√2, √5 ) (square root of two and cubed root of 5) and prove they are the...
Apr24-10 07:07 PM
VKint
1 1,187
Lets try arguing in not mathematical terms but logical reasoning. if a number x is divided by any number n, it means...
Apr23-10 06:21 AM
Mentallic
16 3,367
I am trying to find an example of a diagonal linear operator T in L(H) H is hilbert space that is bounded but not...
Apr22-10 03:50 PM
Landau
1 1,406
Show that if a \equiv b mod p for all primes p, then a = b.
Apr22-10 09:00 AM
HallsofIvy
5 4,745
I am having difficulties with understanding some aspects of inner products. For example, ||u|| = <u,u> Where...
Apr22-10 08:45 AM
HallsofIvy
10 1,881
Hi! Studying the introductory chapters of a Operator Theory book, I have found that the author seem to find a lot of...
Apr21-10 09:18 PM
JSuarez
5 1,295
For the theorem: " If v1,.....,vr are eigenvectors of a linear map T going from vector space V to V, with respect to...
Apr21-10 08:31 AM
HallsofIvy
6 2,352
One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm...
Apr21-10 12:55 AM
radou
3 1,404
Can someone explain to me how to find all the cosets of a set like H={A in GL(n) | det(A) = 1} in GL(n) (set of...
Apr20-10 01:21 PM
Martin Rattigan
6 3,418
Let R = Mn(F) be the ring consists of all n*n matrices over a field F and E = E11 + E22 + ... + En-1,n-1, where Eii...
Apr20-10 01:01 PM
Martin Rattigan
4 1,113
Does anyone have a good resource of worked examples on simple (ish) tensor algebra? By way of background I'm a...
Apr19-10 05:42 AM
bill nye scienceguy!
2 1,465
Why is it that if the sum of the digits of a number is divisible by three, the number itself is also divisible by...
Apr19-10 02:16 AM
Char. Limit
5 2,773
Hi all, Let's say we have a symmetric matrix A with its corresponding diagonal matrix D. If A has only 1...
Apr18-10 02:20 AM
Noxide
4 5,334
Hi I am struggling to get my head fully around the conjugacy classes of D5. Everywhere I have looked seems to...
Apr17-10 01:27 PM
Martin Rattigan
5 8,843
Is there a variant form of induction to prove something about the rationals as opposed to just the natural numbers? ...
Apr17-10 12:24 PM
ramsey2879
2 1,561
This is a theorem about Jacobi symbols in my textbook: Let n and m be ODD and positive. Then (a/nm)=(a/n)(a/m) and...
Apr17-10 12:10 PM
robert Ihnot
1 2,696
Let x and y be elements of a group. I can see that it works the other way, i.e. if x and y commute, then y*x^n =...
Apr16-10 09:54 PM
landor
5 1,677
Amateur question ahead, be warned. I really dislike proofs that something cannot be done. My first gripe is that...
Apr15-10 10:35 PM
CRGreathouse
18 10,691
I think I have worked out a formula for Prime Numbers. I said, "I think," because 1. I dont know , Is that formula...
Apr15-10 12:30 PM
CRGreathouse
7 1,718
Is set theory, counting off members, realy indicative of any order of difference when neither set has a 'size' ? If my...
Apr15-10 08:39 AM
lavinia
14 2,079
Today I was reading in a probabilities textbook that the probability of the union of two events is: p(E_1 \cup...
Apr14-10 03:22 PM
Damidami
0 1,230
I randomly came accross this problem: http://en.wikipedia.org/wiki/Thirty-six_officers_problem however, the...
Apr14-10 02:33 PM
Martin Rattigan
1 2,104
Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!
Apr13-10 05:52 PM
VeeEight
3 1,627

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