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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 35,908
Title says it all really. But basically I'm looking for online info about creating the Leech lattice from the E8...
Jun19-11 03:03 PM
0 853
My understanding of Lie groups is non-existent. But I'm trying to understand if the Leech lattice is a 'lie group?"
Jun20-11 02:55 PM
4 1,580
I just read an article ( saying that multiplication is not repeated...
Jun19-11 06:22 PM
93 16,030
What is the absolute best abstract algebra book for graduate students? I was wanting a book that covers algebra in the...
Jun15-11 09:55 PM
5 3,168
Hi folks, If I have a Lie algebra \mathfrak{g} with an invariant (under the adjoint action ad of the Lie algebra)...
Jun14-11 11:50 AM
2 1,400
I know that any prime p = 1 mod 4 can be expressed as sum of 2 squares. But how many different pairs of integers a,b...
Jun14-11 08:23 AM
robert Ihnot
7 2,850
Hi all, I have been trying to gain a deeper insight into quadratic forms and have realised that my textbook makes...
Jun19-11 12:43 PM
14 2,745
I'm trying to find out what the rotation group of a cube is. It seems natural to view it as a subgroup of S_{6},...
Jun16-11 03:47 PM
18 5,457
Hi, Algebraists: Say I'm given a group's presentation G=<X|R>, with X a finite set of generators, R the set of...
Jun18-11 07:13 PM
2 1,118
i want to extend the set S={(1,1,0,0),(1,0,1,0)} to be a basis for R4. I know I am going to need 4 vectors, so i need...
Jun18-11 04:07 PM
6 6,630
I want to express the matrix product Ax as a linear combination of the column vectors in A. I know for that for...
Jun13-11 08:17 PM
5 5,238
if i have a 4x3 matrix, this means there are more equations than unknowns and so there are no solutions to the system....
Jun14-11 03:19 AM
3 2,611
Hello all :) I am studying divisibilities of 1, 11, 111, 1111, 11111 and so on when I have even number of 1s, in...
Jun13-11 08:46 PM
2 1,554
Hi, yet another question regarding polynomials :). Just curious about this. Let f(x), g(x) be irreducible...
Jun15-11 08:21 PM
5 1,406
In the book I am looking only one of the following is listed as a Jordan Form. Could somebody tell me why the other...
Jun15-11 07:05 PM
5 1,146
I have a non-homogeneous Ax=b (with b non-zero) and i want to know if the set of all the solution vectors, x, forms a...
Jun14-11 04:03 AM
2 2,334
I came across this question. How do you show that √N is irrational when N is a nonsquare integer? Cheers.
Jun16-11 07:12 AM
2 2,302
I have a question I need to resolve before my exam on thursday. It relates to the following result: Let N be a...
Jun14-11 01:25 PM
2 1,177
Hello, I am trying to solve a Pell's equation X2 + 2Y2 =1 I understand that the (3,2) is a fundamental...
Jun19-11 10:47 AM
6 2,561
The prime number theorem describes the distribution of the prime numbers, in a sense. Are there other prime number...
Jun15-11 08:12 PM
2 1,815
Hello :) I have been giving a mathematical problem. But I find difficulties solving this. Therefore, I will be very...
Jun16-11 08:21 AM
12 2,248
Consider the spectral decomposition , let Gj=xjyjT for j=1,2,3 ,n so that A=sigma (mjGj) . a-Show that each...
Jun15-11 11:11 AM
0 849
Show that the representation of T with respect to the basis {x1,x2,x3, xn} where xi belong toSi (1 less i less ...
Jun15-11 11:13 AM
0 788
Consider a) f1=1, f2=sinx , f3=cosx b) f1=1, f2=ex , f3=e2x ...
Jun15-11 11:30 AM
1 882
If \omega is an alternating tensor, then Alt(\omega)=\omega, where Alt is the mapping that maps any tensor to an...
Jun15-11 02:52 PM
1 885
Okay, I know that if I can't get n linearly independent eigenvectors out of a matrix A (∈ℝnxn), it is not...
Jun19-11 06:06 AM
3 1,951
Given two orthonormal bases v_1,v_2,\cdots,v_n and u_1,u_2,\cdots,u_n for a vector space V, we know the following...
Jun17-11 01:44 AM
I like Serena
6 1,573
such as some 3D matrix visualization or eigenvalue/singular value things/jordan form? Thanks very much for any...
Jun18-11 10:01 AM
Stephen Tashi
1 1,702
I'm wondering why 1/k! is needed in Alt(T), which is defined as: \frac{1}{k!}\sum_{\sigma \in S_k} \mbox{sgn}\sigma...
Jun18-11 10:13 PM
2 1,213
Is saying \existsx, \existsy the same as saying \existsy, \existsx?
Jun17-11 10:54 PM
2 1,714
Outside of pure mathematics, where is group theory used?
Jun18-11 09:54 PM
6 2,419
If Riemann's Hypothesis is proved as true, would number theory collapse?
Jun18-11 08:20 AM
3 1,797
"orthonormal columns imply orthonormal rows for square matrix." My proof is: Q^{T}Q=I(orthonormal columns)...
Jun18-11 03:53 AM
1 954
i have ordered introduction to linear algebra by gilbert strang.But i saw it on google books and found it to be...
Jun18-11 09:53 PM
2 3,385
Other than the Eucledean method (1+p1p2p3...)and so on other than this, how do we prove that there are infinte...
Jun20-11 11:46 AM
10 3,041
Hi all, I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using...
Jun18-11 02:29 PM
0 1,427
Sorry if this is a well known thing, but I've noticed this and decided to see how well known it is, also if there is a...
Jun19-11 10:14 PM
2 2,683
Is it true that every matrix is similar to its transpose? A claim in Wikipedia... (field is alg. closed)
Jun20-11 10:27 PM
4 1,829
A non-zero alternating tensor w splits the bases of V into two disjoint groups, those with \omega(v_1,\cdots,v_n)>0...
Jun20-11 02:18 PM
1 1,235
Hi, All: Could someone please tell me or give me a ref. on the basic properties of Gl(n,R) ; R a ring;...
Jun20-11 08:34 PM
2 1,509

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