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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 need to write a code to convert a symmetic matrix into tridiagonal form and am planning to use the...
Mar24-12 12:41 PM
13 2,977
If A = {(x,y) : x = y = e, yx = xˉy} and B = {(u,v) : u^4 = v = e, vu = uˉv}, how do I go about finding the...
Mar28-12 12:02 AM
1 2,270
true or false .. The system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R) is not a field under matrix addition (+)...
Mar28-12 07:39 AM
1 748
Here is an algorithm very simple to find a common factor to a and b. An example : a=867 b=1989 1. We compute...
Mar18-12 07:38 PM
20 3,000
Hey, i've been trying to find a better fit for a correlation, the numbers i'm dealing with are really small and when...
Mar21-12 11:27 AM
Stephen Tashi
1 1,885
Hello Everyone :) I have been facing a little difficulty when encountering such kind of problems . i have also...
Mar19-12 07:56 PM
8 1,202
How do I show that for any vectors u,v, and w in a vector space V, the set of the vectors {u-v, v-w, w-u} is a...
Mar19-12 11:39 AM
6 2,952
Q. Given that A is invertible , check whether A + A^(-1) is invertible or not ? A. A is invertible . => A^-1 exists...
Mar21-12 08:03 AM
13 1,713
Hello I have this Hamiltonian: \mathcal{H} = \alpha S_{+} + \alpha^{*}S_{-} + \beta S_{z} with \alpha,...
Mar19-12 09:08 AM
0 1,247
Hi i found a question in number theory, involving two equations, it goes as follows: Let p1, p2, p3 and p4 be 4...
Mar19-12 06:11 PM
1 2,266
I think I found a procedure (other than the extended Euclidean algorithm) to compute the multiplicative inverse of a...
Mar20-12 05:20 AM
0 1,392
Hi everyone, I always have trouble on decomposing number into irreducible factors inside Gaussian integer field. I...
Mar21-12 05:50 AM
3 1,080
This is dealing with computer vision, but the only part I'm having trouble understanding is a step in the matrix math....
Mar23-12 01:33 AM
Stephen Tashi
6 1,460
I got one example on my notes about PID and maximal ideal. I feel it is a strange example as it doesn't make sense to...
Mar21-12 10:12 AM
2 1,385
Firstly, I am not sure if I am in the right section. Pardon me. I was reading something related to computational...
Mar22-12 07:57 AM
9 3,008
We learned the GSP yesterday in class, but my teacher said something that seems to conflict with the textbook. He...
Mar21-12 10:06 AM
1 894
I have some questions about spanning sets 1. Why does empty set spans the zero subspace? 2. Why is this true:...
Mar21-12 10:41 AM
5 969
Hi, I know next to nothing about abstract algebra (had one intro-class years ago), so sorry if this is a dumb...
Mar22-12 03:10 PM
5 1,295
I am readin Belinte's book about Lie algebras (I have also the Cahn) . And I try to understand this. He writes ...
Mar23-12 11:38 AM
2 868
Some algorithms of finding the eigenvalues of symmetric matrices first transform the matrix to a tridiagonal matrix...
Mar22-12 08:07 PM
2 1,540
Hi, I am told to give the subgroup H=<α,β> with α,β\inS3 α = (1 2) β = (2 3) So I know that H={αkβj|j,k\in(the...
Mar22-12 10:44 PM
1 1,683
Say i have the following function: f(x)= {-45 , x<0.5 45 , x≥0.5} where x\in R is a real variable in ....
Mar23-12 12:20 AM
3 1,941
I asked this question on one another forum but didn't get any answer . Consider the following array of natural...
Mar27-12 11:02 AM
7 2,423
When we talk about an abstract binary operation *:SxS --> S We say that an identity element "e" exists when e * x =...
Mar23-12 11:42 AM
2 964
I did these years ago. I remember that there used to be an order, that if you followed, you always got the answer. ...
Mar23-12 01:26 PM
0 807
Given n by n matrices A, B, C. I know how to solve the Sylvester equation AX + XB + C = 0 using the matlab...
Mar26-12 03:24 AM
3 1,630
hello :) I was trying to prove the following result : for a linear mapping L: V --> W dimension of a domain V =...
Mar27-12 06:29 AM
5 1,187
Is it true that SO(3) has no complex 2-dimensional representation (except the trivial one...)? How to see this? If it...
Mar24-12 06:40 PM
2 1,141
Let a, b, and c be elements of group <G, *>, then Can we apply cancellation law here: a*b = c*a??? I could prove...
Mar24-12 11:22 PM
8 1,591
Hi, All: I have been tutoring linear algebra, and my student does not seem to be able to understand a...
Mar25-12 09:51 PM
5 1,072
I'm completely lost on this one. I need this to be able to solve that the square root of three is irrational. So it's...
Mar26-12 04:55 PM
4 1,957
Hello, it's been a while since i did linear algebra. i need some help. I have this matrix: 1 1 0 0 1 0 0 0...
Mar25-12 08:34 PM
1 1,569
Hi Everyone, I am kind of looking some online text to understand Lie Algebra, Group Theory and so forth. I usually...
Mar27-12 08:39 PM
9 1,758
Suppose a (n x 3) matrix B is given, n>3. Also, suppose a matrix (3 x 3) matrix C is given, whose columns correspond...
Mar26-12 02:58 AM
1 1,003
How the hell do you prove that the components of a vector w.r.t. a given basis are unique? I have literally no idea...
Mar26-12 01:38 PM
3 921
While studying groups, Is there a common pattern/arrangement of the group elements represented in a table? Is...
Mar27-12 03:55 PM
Number Nine
9 953
Well, I have solved this problem from a textbook: Prove the Schwarz inequality. When you try to solve it, you...
Mar27-12 05:50 AM
1 768
This seems a simple question but I can't find the solution by myself. Please help. Say we have a 2 by 2 matrix with...
Mar27-12 06:06 AM
2 2,823
He starts using the term 'reducible', as it came out of nowhere, from the page 162 of the text. I know, roughly,...
Mar27-12 04:49 PM
2 826
I intend to use the Gershgorin Circle Theorem for estimating the eigenvalues of a real symmetric (n x n) matrix....
Mar28-12 02:48 AM
0 1,052

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