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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 36,232
What interpretation could the eigenvectors in a graph have? By graph I mean an adjaceny matrix not counting...
Jun13-11 08:11 PM
1 1,712
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 3,219
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 1,417
For any natural number a and b, with b > 1, two natural numbers x and y can always be found such that b^x - b^y is...
Jun13-11 01:10 AM
5 2,485
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 2,877
Hi, Is every matrix similar to a triangular matrix? If it is, anyone have an idea how to prove it? Thanks
Jun13-11 03:37 AM
3 1,307
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 5,590
With normal vectors i usually check there is the correct number of vectors i.e 3 for R3 2 for R2 etc and then just...
Jun12-11 07:11 AM
10 2,190
Hi, I have this problem, 1) Find 1 + 2 + + n by summing the identity (m + 1)2 − m2 = 2m + 1 from m = 1 to...
Jun12-11 10:31 PM
2 1,899
Suppose that the set of functions \{P^a:\mathcal S\rightarrow \mathcal L|\,a\in \mathcal L\} has the property that for...
Jun11-11 07:26 PM
2 671
does multiplying the invertible matrix A to the basis {X1,X2,X3..Xn} create a new basis; {AX1,AX2,Ax3..AXn}? where Xn...
Jun13-11 02:48 AM
4 1,821
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 6,705
Hey everyone, Not sure if this is the right section to post this in, but makes the most sense to me so here goes. ...
Jun11-11 10:52 PM
0 1,226
Hi, I'm currently doing a project and this topic has come up. Are there any known famous classes of polynomials...
Jun12-11 01:18 PM
8 1,307
\lambda_i(AB)\leq\lambda_i(A)\lambda_i(B)? \lambda_i(A+B)\leq\lambda_i(A)+\lambda_i(B)?...
Jun13-11 02:10 AM
0 696
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 5,385
lets assume the matrix multiplication AB exists, how would i prove that the column space of AB is contained in the...
Jun13-11 03:01 AM
3 4,357
For two matrices A and B, when p(A)=0 iff p(B)=0 for any polynomial, what will happen? i read that A and B have the...
Jun13-11 02:13 PM
2 1,282
Hi! Q is postive definite A is any matrix. Why Q^{-1}AQ^{-1} is hermitian??
Jun13-11 04:17 AM
1 661
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 2,659
If S^{-1}BS=A, can we always find Q ,such that Q^{-1}BQ=A? Q different form S and no scalar multiple of S. If not,...
Jun13-11 05:54 AM
1 689
Hi folks. This is something I've been wondering about for a while now. Is there a reason why taking the minimum norm...
Jun13-11 10:23 AM
1 835
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 1,558
Hi, yet another question regarding polynomials :). Just curious about this. Let f(x), g(x) be irreducible...
Jun15-11 08:21 PM
5 1,419
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 1,156
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 2,364
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 2,322
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 1,190
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 1,835
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 2,262
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
0 855
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
0 794
Consider a) f1=1, f2=sinx , f3=cosx b) f1=1, f2=ex , f3=e2x ...
Jun15-11 11:30 AM
1 889
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
1 893
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 1,597
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 1,725
Is saying \existsx, \existsy the same as saying \existsy, \existsx?
Jun17-11 10:54 PM
2 1,725
If Riemann's Hypothesis is proved as true, would number theory collapse?
Jun18-11 08:20 AM
3 1,815
"orthonormal columns imply orthonormal rows for square matrix." My proof is: Q^{T}Q=I(orthonormal columns)...
Jun18-11 03:53 AM
1 964
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 1,446

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