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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 35,758
Hi: Given a fin.dim vector space V over R, and two different bases B_V,B_V' for V , we say that B_V,B'_V are...
May6-10 11:18 AM
lavinia
1 1,151
Is there anyway to show that for a symmetric or normal matrix A, that det(A) = \prod \lambda_i without using Jordan...
May6-10 07:26 AM
HallsofIvy
4 1,189
Hi there! I'm trying to prove the following obvious statement, but am somehow stuck :( Let \vec a,\ \vec...
May5-10 10:42 PM
Live2Learn
4 1,883
So it says here "Let S be a set of sets. Show that isomorphism is an equivalence relation on S." So in order to...
May5-10 03:03 PM
yaganon
2 812
First what are Idempotents? Second, If A and B are simliar matrices, show that if A is idempotent then so is B.
May5-10 09:38 AM
Landau
3 1,024
Is this possible? I've computed a multiobjective least squares solution and want to make it able to be updated...
May5-10 06:06 AM
jasonRF
1 1,449
What is the difference between a homomorphism which is from a group G ONTO a group H and a homomorphism which is from...
May4-10 11:20 PM
swartzism
28 8,868
So this is supposed be an introductory problem for tensor products that I was trying to do to verify I am...
May4-10 04:45 PM
TMM
7 2,564
For the linear transformation, T: R^2\rightarrow R^2, T(x,y) = (x^2,y) find the preimage of.. f(x)= 2x+1 I...
May3-10 08:53 AM
HallsofIvy
2 1,361
Hi... How do I construct a Galois extension E of Q(set of rational numbers) such that Gal is isomorphic to Z/3Z. ...
May2-10 09:11 PM
TMM
5 2,673
1: Is a group of permutations basically the same as a group of functions? As far as I know, they have the same...
May2-10 04:36 PM
Martin Rattigan
5 2,567
Is the lifting of an algebraic extension also algebraic? i.e. K,E are extensions of F, E algebraic over F, KE...
May2-10 10:46 AM
qddwwzh
0 794
Hi... We have all seen the equation det(M)=exp(tr(lnM)). I was taught the proof using diagonalisation. I was...
Apr30-10 11:17 PM
Simon_Tyler
4 8,766
I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one,...
Apr30-10 04:11 AM
astroultraman
20 7,249
Let A be an n x n matrix with eigenvalue \lambda . Prove that \lambda ^2 is and eigenvalue of A^2 and that if v is an...
Apr29-10 08:53 PM
Evo
3 863
Hi, I'm reading Shankar's Principles of QM and I find it not very clear on how exactly should I change basis of...
Apr28-10 09:23 PM
Fredrik
3 1,558
Hi, what I did to try to find prime numbers was this (in a computer program) Starting from 2, I set off a sine wave...
Apr28-10 08:18 PM
glengarry
8 2,211
I have the following problem: A * Phi = Ax' * Sx + Ay' * Sy where, A= Ax' * Ax + Ay' * Ay + Axy' * Axy and...
Apr28-10 02:52 PM
jasonRF
8 4,406
Could someone please explain how to go about putting an equation in to quadratic form. e.g:...
Apr28-10 08:08 AM
CompuChip
2 2,829
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
3 843
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 3,638
Hi, everyone. I have a question about geometric constructible numbers. I know that "if 'a' is constructible then...
Apr27-10 07:37 PM
emptyboat
2 936
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 1,928
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 3,518
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 10,195
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
2 779
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 5,265
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 5,225
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 1,046
(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 6,074
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 1,010
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 14,997
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 1,358
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 5,142
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 3,576
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 1,011
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 1,197
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 3,378
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 1,418
Show that if a \equiv b mod p for all primes p, then a = b.
Apr22-10 09:00 AM
HallsofIvy
5 4,777

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