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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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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 30,412
G,H be groups(finite or infinite) Prove that if (G:H)=n, then there exist some normal subgroup K of G (G:K)≤n!...
Mar22-10 08:23 AM
3 1,144
Need to find all the posible solutions (a,b,c) for 1/a + 1/b + 1/c = 1, a,b,c integers.
Mar22-10 04:56 AM
14 17,016
Hi there, just a pretty straight forward query I need cleared up..... If a question asks for the null space of A...
Mar22-10 02:07 AM
2 702
Hi guys, I'm trying to show that \mathbb{F}_5/(x^2+2) and \mathbb{F}_5/(x^2+3) are isomorphic as rings. As I...
Mar21-10 08:54 AM
4 1,127
How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the...
Mar20-10 08:44 PM
3 1,008
hey guys, im a student engineer and have found that the laws we use are primarily based off of stats. this has led me...
Mar20-10 01:37 AM
10 1,844
Hello, Let's consider the L^2(\mathbb{R}) space with an inner product, and the complex sinusoids in the interval...
Mar19-10 04:09 PM
5 2,355
I'm an undergraduate computer-science student doing research in the field of computer vision, and one of the tasks...
Mar19-10 07:06 AM
1 3,693
Hello people. I'm a freshman in college and I'm looking forward to enter an advanced mathematics program. The...
Mar18-10 01:26 PM
9 7,854
If I want to know how many solutions a consistent linear system with more equations than unknowns has, how do I tell?...
Mar18-10 06:49 AM
1 3,216
hi, i was reading about finitely generated ideals and there was a remark that ideal which consists of...
Mar18-10 05:12 AM
1 1,520
hi, i want to show that If R is a PID then a submodule of a cyclic R-module is also cyclic. do i need to use...
Mar17-10 08:33 PM
2 2,035
I am having the hardest time proving that "The product of any two even integers is a multiple of 4." My proof...
Mar17-10 04:02 PM
1 1,210
Proving Axiom 1 of all 3 x 3 magic squares. I used summation notation to do so but it is extremely long and...
Mar17-10 09:31 AM
4 1,331
How to prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A....
Mar17-10 09:10 AM
2 1,058
If A\in O(3) and v,w\in\mathbb{R}^3, then (Av)\times (Aw) = (\textrm{det}\;A) A(v\times w) is right, right?...
Mar16-10 03:08 PM
7 3,183
Take two rows of respective length m and n: a1, a2, a3,..., am and b1, b2, b3, ..., bn. Then produce as follows...
Mar16-10 02:11 PM
6 1,361
Hey guys! I am having a major brain problem today, with this problem. L is a linear transform that maps...
Mar16-10 11:03 AM
4 3,074
Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an...
Mar16-10 10:53 AM
0 1,014
Hey I'd appreciate it if somebody could "yay or nay" my understanding of the following concepts, I think I'm mixing...
Mar15-10 06:46 PM
4 948
See the attachment/// Can Anyone Understand this??? I mean what metod has he followed to solve this equation for x...
Mar14-10 07:28 PM
2 834
given the sequence (power series) g(x)= \sum_{n\ge 0}a(n)(-1)^{n}x^{n} if i define ...
Mar14-10 01:42 PM
3 1,243
Hi everybody, I'm new to absract algebra and I really can not understand different between direct sum and direct...
Mar14-10 11:58 AM
9 7,008
So an example was the matrix: A = \left(\begin{array}{cccc} a&a+b\\ b&0\\ \end{array} \right) is a...
Mar14-10 11:52 AM
2 2,275
Definition: A primitive Pythagorean triple is a triple of natural numbers x,y,z s.t. x^2 + y^2 = z^2 and gcd(x,y,z)=1....
Mar14-10 07:13 AM
8 3,681
Hi, I've been trying to get my head around this. \Sigma_{(j)} is a p x p matrix given by \Sigma_{(j)} =...
Mar14-10 04:04 AM
4 6,289
WITHOUT using the MATLAB ‘MULTIPLICATION COMMAND’ write down your own program to implement the matrix multiplication M...
Mar13-10 04:40 PM
1 1,740
I quite like the following definition of pi and I wonder which minimal algebraic rules are needed to make this...
Mar13-10 09:40 AM
2 1,049
e_r=\#\lbrace d:d\mid n\;\;\; \textup{and}\;\;\; d=p_r^k, k\in N\rbrace where n=p_r^{e_r} I am using it in a...
Mar12-10 11:31 PM
4 1,133
I am reading an Abstract Algebra book, and there is a theorem that says: Thm: If G is a finite group, then the...
Mar12-10 09:52 PM
1 1,047
"Let p be an odd prime, then we proved that the Legendre symbol ...
Mar12-10 08:11 PM
robert Ihnot
12 4,146
Hi Everyone, I am reading up on information theory, and every resource I have found on the topic which derives the...
Mar12-10 07:29 PM
5 1,250
Hi... I need a program that can give me all the subgroups of a group that I define. I also need it to give me the...
Mar12-10 02:55 AM
krishna mohan
2 1,300
does the floor function satisfy floor(x)= x + O(x^{1/2}) the idea is the floor function would have an 'smooth'...
Mar11-10 08:15 PM
7 2,041
nevermind, please delete
Mar11-10 04:35 PM
0 1,005
This may seem like a very obvious question, but I thought it may be some sort of trick that my lecturer thought I may...
Mar11-10 09:25 AM
1 2,384
So I am working on solving sets of linear congruence with the chinese remainder theorem. When I go to solve for the...
Mar10-10 05:46 PM
2 2,226
So I have a couple of questions in regards to linear operators and their eigenvalues and how it relates to their...
Mar10-10 11:57 AM
5 2,896
I am having trouble with this proof: show that if d|n then phi(d)|phi(n). I know that if d|n, then ad=n and that...
Mar10-10 11:21 AM
7 3,841
I have the following equation: (k(x)*g(x)')'=p*g(x) where k(x) = k(x+T) -- k(x) is a known periodical function...
Mar10-10 07:47 AM
1 906

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