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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 34,257
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 5,108
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 3,535
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 1,000
how do I find all u in R such that Q(u)=Q(√2,³ √5 ) (square root of two and cubed root of 5) and prove they are the...
Apr24-10 07:07 PM
VKint
1 1,177
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 3,361
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 1,405
Show that if a \equiv b mod p for all primes p, then a = b.
Apr22-10 09:00 AM
HallsofIvy
5 4,739
I am having difficulties with understanding some aspects of inner products. For example, ||u||² = <u,u> Where...
Apr22-10 08:45 AM
HallsofIvy
10 1,876
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 1,290
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 2,350
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 1,401
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 3,410
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 1,105
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 1,461
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 2,690
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 5,314
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 8,826
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 1,554
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 2,691
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 1,614
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 10,667
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 1,716
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 2,060
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 1,180
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 2,096
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 1,352
Hi, I was wondering why the wave-function in quantum mechanics is complex. There are a lot of threads in the...
Apr13-10 04:37 PM
IanC89
6 1,073
A= (3 0 0 3 ) why is it diagonalizable? i'm not sure...
Apr13-10 08:13 AM
Rajini
1 874
can any body please give me matlab version 6 coding of gauss jordan elimination method or how to make following gauss...
Apr13-10 07:37 AM
hell_demon
0 2,646
Let R = Mn(F) the ring consists of all n*n matrices over a field F and E = E11 + E22 + ... + En-1,n-1, where Eii is...
Apr13-10 05:21 AM
xixi
0 609
"11 and 101 are primes, whereas 1001 is not (7*11*13). Find the next smallest prime of the form 100...01, and show...
Apr12-10 07:03 PM
CRGreathouse
21 6,098
Hello math goers, My education in linear algebra is limited to an Intro course I took a year ago. So I am posting...
Apr12-10 05:34 PM
Xuser
3 1,165
Say you have two vectors v_1 and v_2 in \Re^3. Then the area of the parallelogram generated by these two vectors is...
Apr12-10 05:21 PM
mbs
1 961
Hi all, Can anyone please help me with the following question. Actually, i received a paper from some German...
Apr12-10 02:00 PM
seth001
0 714
Can an element of a quotient group G/N in an isomorphism f:G/N--H map back onto itself if it does not have a...
Apr12-10 10:35 AM
rs1n
1 693
hello, if i have a sequence of definite positive matrices that converges, is it always that the limit matrix is...
Apr12-10 09:24 AM
damix
1 1,172
how does one convert a vector equation of a plane to a scalar equation. This is given the parametric equations of the...
Apr12-10 09:00 AM
HallsofIvy
2 2,795
Hello. Let´s suppose we are given two subspaces of \mathbb{R}^n that have dimension k, where 1\leq k<n. I think they...
Apr12-10 01:41 AM
mnb96
2 1,901
Ok so I've been working on this problem and I'm really having some struggles grasping it. Here it is: Let W be...
Apr11-10 11:45 PM
Bacle
3 1,031
How to prove that if A is upper triangular and B is the matrix that results when the ith row and jth column of A are...
Apr11-10 07:01 PM
Bacle
1 755

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