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Linear & Abstract Algebra

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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 30,401
I saw in an application of Sylow's theorems, it said we have something like a group of order 28 = 2^2 x 7, so we have...
Oct15-09 04:46 PM
jbunniii
1 849
How much can a determinant tell you about the entries of a matrix? How much more if you know the size of the...
Oct15-09 03:37 PM
jasonRF
3 991
Prove that if A is an invertible matrix and AB = BC then B = C. I thought the way to approach it was to use A^-1 on...
Oct15-09 06:56 AM
HallsofIvy
1 6,844
The complexified Lie algebra of the Lorentz group can be written as a direct sum of two commuting complexified Lie...
Oct14-09 10:57 PM
aziz113
1 976
to begin I am wondering if its even true that they are equal. As i lost the sheet with that on it. If that is not true...
Oct14-09 09:00 PM
lstellyl
1 3,190
Greetings PF, I would like to sketch the proof that Abel gave for the insolubility of the quintic. This is a...
Oct14-09 07:23 PM
icantadd
2 1,748
Does anyone know where I can access past exam papers in the field of linear algebra. I am particularly looking for...
Oct14-09 08:49 AM
Dafe
4 10,021
I am in a linear algebra and differential equations course and have recently been learning how to find a basis for a...
Oct14-09 06:52 AM
HallsofIvy
4 2,975
Hi all! I was working on some homework for the linear algebra section of my "Math Methods for Physicists" class and...
Oct14-09 03:00 AM
Matthollyw00d
2 9,709
I'm having trouble understanding just what is the difference between the three types of maps: injective, surjective,...
Oct13-09 03:56 PM
Moo Of Doom
4 4,456
Looking for info on game theory
Oct12-09 01:49 AM
robert Ihnot
3 1,596
Hey guys, new to the forum but hoping you can help. How do you prove that vector spaces V and U have a linear...
Oct11-09 10:43 PM
Servarus
6 3,243
I'm working on trying to figure this proof out but its proving to be quite difficult does anyone have any insight? ...
Oct11-09 02:30 PM
Office_Shredder
1 4,219
I was wondering if anyone could give me some hints on this Suppose A^k=0 for some integer k is greater than or...
Oct11-09 07:27 AM
HallsofIvy
2 792
Greetings, I am faced with a problem in Group Theory. It's not homework. I am trying to study it by myself. The...
Oct10-09 05:25 PM
Jösus
2 2,045
Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s...
Oct10-09 04:40 PM
Jösus
1 893
Hello, I am quite new here, as my number of posts might indicate. Thus I am not really sure whether or not this...
Oct10-09 04:00 PM
Jösus
2 1,263
Hello, how would you solve an homogeneous system of the form A\mathbf{x}=0, with the constrain...
Oct10-09 09:27 AM
Hurkyl
5 621
Hello, I'm trying to use either MAXIMA or MATLAB for extended polynomial division. In MAXIMA, I can use the...
Oct8-09 11:46 PM
EBMath
0 2,347
Let V be a vector space and let T: V \rightarrow V be a linear transformation. Suppose that n and k are positive...
Oct8-09 02:38 PM
tiny-tim
1 1,171
Hi, I have a (markov chain) transition matrix X which I understand. In particular each row of this matrix sums to...
Oct8-09 08:10 AM
g_edgar
5 4,508
1. The problem statement, all variables and given/known data How do I show that the cp is p(x)=x^n, dimA=n? 2....
Oct8-09 07:10 AM
trambolin
7 4,908
I have a system that ideally creates a real symmetric negative definite matrix. However, due to the implementation of...
Oct8-09 03:33 AM
trambolin
3 1,504
Hello, given a vector x=(a,b) in 2D, and considering another vector obtained by shifting cyclically the coordinates...
Oct7-09 01:38 PM
mnb96
12 1,351
Give one primitive element for each of the finite field: F2n (here "2" is the subscript) for n=1, n=2,...,n=8
Oct7-09 07:23 AM
tiny-tim
1 656
I need to calculate eigen values and eigen vectors of a large symmetric real matrix, but all eigen vectors have to be...
Oct7-09 07:13 AM
Born2bwire
3 2,319
Hello, I was trying to follow a proof that uses the dot product of two rank 2 tensors, as in A dot B. How is...
Oct6-09 12:42 PM
dakg
5 15,255
I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k....
Oct6-09 08:04 AM
CRGreathouse
1 1,906
I'm considering the problem: Given c \in \bold{F}, v \in V where F is a field and V a vector space, show that cv = 0,...
Oct6-09 06:47 AM
Landau
7 1,694
Prove that: g is a generator of Fp* if and only if g^(p-1) = 1 (mod p) and gq ≠ 1 (mod p) for all prime divisors q...
Oct6-09 04:28 AM
Hurkyl
1 662
The parabola y = x2 is rotated anti-clockwise about the origin through the angle 30o. What is the new equation of the...
Oct5-09 07:26 PM
HallsofIvy
2 710
Hello, so i was looking up the defintion of linear mapping and mapping in general and i have seen the technical...
Oct5-09 07:24 PM
HallsofIvy
1 948
I'm going through Axler's book and just got introduced the concept of sums of subspaces and the direct sums. Here's...
Oct5-09 02:43 PM
jeffasinger
5 3,733
given the formula g(x)= \sum_{n \le x} has any meaning in number theory ? ,
Oct5-09 09:42 AM
ramsey2879
1 1,434
prove Byron's Conjecture. Define the set Znx={k∈Zn but not including zero :gcd(k; n) = 1} (a) Prove that Znx is a...
Oct2-09 01:49 PM
g_edgar
3 1,153
Ok... So today, someone asked me a simple question: Why do two negatives become a positive number when multiplied...
Oct2-09 09:57 AM
Whatever123
8 1,641
Recall the definition of n! (read n factorial"): n! = (n)(n-1)(n-2) ….(2)(1) =∏(k) In both (a) and (b) below,...
Oct2-09 01:40 AM
robert Ihnot
2 1,746
So I have this code: function ApproxSinDeriv(x,n) h=.5; for i = 0:n h; approx =...
Oct1-09 12:18 PM
Providence88
2 1,740
Is it possible to find a formula to expand this polynomial: (n+1)(n+2)\ldots(n+x) where n,x\in\textbf{N}. In other...
Oct1-09 08:28 AM
Bingk
6 1,891
Let Q: R3 \rightarrow R be the quadratic form given by Q(x) = 2x1x2 + 2x1x3 + 2x2x3 where x = (x1x2x3)t How do I...
Sep30-09 08:12 PM
squenshl
1 897

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