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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 35,127
What interpretation could the eigenvectors in a graph have? By graph I mean an adjaceny matrix not counting...
Jun13-11 08:11 PM
Ackbeet
1 1,661
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
ForMyThunder
5 3,083
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
SergejVictorov
2 1,382
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
marshmellow
5 2,446
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 2,803
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
td21
3 1,286
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
lpetrich
18 5,340
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
HallsofIvy
10 2,123
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
bluemoon2188
2 1,851
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
Fredrik
2 657
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
mitch_1211
4 1,746
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
Bacle
6 6,544
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
Xian
0 1,215
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
burritoloco
8 1,279
\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
td21
0 677
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
Mark44
5 5,117
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
td21
3 4,206
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
HallsofIvy
2 1,264
Hi! Q is postive definite A is any matrix. Why Q^{-1}AQ^{-1} is hermitian??
Jun13-11 04:17 AM
dragonlorder
1 644
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
td21
3 2,564
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
henry_m
1 673
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
HallsofIvy
1 825
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
l-1j-cho
2 1,540
Hi, yet another question regarding polynomials :). Just curious about this. Let f(x), g(x) be irreducible...
Jun15-11 08:21 PM
burritoloco
5 1,385
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
Zorba
5 1,130
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
td21
2 2,295
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
bgwyh_88
2 2,271
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
Zorba
2 1,145
The prime number theorem describes the distribution of the prime numbers, in a sense. Are there other prime number...
Jun15-11 08:12 PM
hansenscane
2 1,792
Hello :) I have been giving a mathematical problem. But I find difficulties solving this. Therefore, I will be very...
Jun16-11 08:21 AM
micromass
12 2,215
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
bernoli123
0 839
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
bernoli123
0 776
Consider a) f1=1, f2=sinx , f3=cosx b) f1=1, f2=ex , f3=e2x ...
Jun15-11 11:30 AM
micromass
1 875
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
Office_Shredder
1 872
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 1,546
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 1,668
Is saying \existsx, \existsy the same as saying \existsy, \existsx?
Jun17-11 10:54 PM
gmmstr827
2 1,690
If Riemann's Hypothesis is proved as true, would number theory collapse?
Jun18-11 08:20 AM
Karlx
3 1,772
"orthonormal columns imply orthonormal rows for square matrix." My proof is: Q^{T}Q=I(orthonormal columns)...
Jun18-11 03:53 AM
Fredrik
1 940
Hi all, I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using...
Jun18-11 02:29 PM
kaizen.moto
0 1,413

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