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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 35,947
In algebra, do you just base your understanding off the pure definitions and groups? I am learning some multilinear...
May10-10 11:03 AM
6 1,728
I have started learning Lie algebra and I can't understand one example given in the notes. Given: = 2 e_{\alpha} ...
May9-10 09:12 PM
1 805
Find smallest d=2a^2=3b^3+2=5c^5+3 where a,b,c are integers. This problem is very hard. Either no solution or d...
May9-10 11:23 AM
2 1,774
Please can someone kindly inform me if significant autocorrelation in stock price returns is enough evidence to...
May8-10 11:28 AM
0 954
Is there any criterion for the irreducibility of a polynomial in several variables over an algebraically closed field...
May8-10 03:04 AM
5 3,369
I admit I had this problem on a set, but it's since been due and no one was able to solve it. I've not cracked it...
May7-10 10:26 PM
0 1,767
I would like a reference for a purely algebraic proof of the fundamental theorem of algebra - or if you would like to...
May7-10 05:32 PM
16 2,866
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
1 1,154
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
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
4 1,893
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
2 816
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
3 1,028
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
1 1,452
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
28 8,917
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
7 2,573
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
2 1,365
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
5 2,686
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 2,577
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
0 799
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
4 8,808
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
20 7,286
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
3 867
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
3 1,571
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
8 2,219
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
8 4,429
Could someone please explain how to go about putting an equation in to quadratic form. e.g:...
Apr28-10 08:08 AM
2 2,844
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
3 846
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 3,650
Hi, everyone. I have a question about geometric constructible numbers. I know that "if 'a' is constructible then...
Apr27-10 07:37 PM
2 940
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
1 1,942
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 3,529
hi, i don't really understand whats the difference between vector product and dot product in matrix form. for...
Apr27-10 11:42 AM
6 10,223
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
2 781
Hello, I'm a senior mechanical engineering student. I'm trying to write an application that plots the system...
Apr27-10 04:05 AM
14 5,277
Hi, is there any numerical invariant that would characterize the rank of a non-square matrix, similar to the...
Apr27-10 04:03 AM
5 5,256
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
2 1,050
(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
8 6,104 AFAIK logic is all about "T"/"F" or 0/1, and boolean...
Apr26-10 02:14 PM
3 1,014
I need to compute the 3 eigenvalues and 3 eigenvectors of a symmetric 3x3 matrix, namely a stress tensor,...
Apr26-10 01:05 PM
8 15,056
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
5 1,360

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