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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 30,424
Hi guys, Let's say I have a 6x6 matrix A whose Jordan form J has 3 Jordan blocks. It means that this matrix (matrix...
Dec3-12 10:24 PM
18 2,734
How are orbits and cosets related? Are all orbits cosets? Are all cosets orbits? Also, what exactly are G-sets and...
Nov30-12 10:09 AM
1 1,041
Linear transformation f:C^∞(R) -> C^∞(R) f(x(t)) = x'(t) a) I have to set up the eigenvalue-problem and...
Nov27-12 08:16 PM
2 927
Hello, I want to find a family of functions \phi:\mathbb{R} \rightarrow \mathbb{C} that have the property:...
Nov28-12 03:30 PM
14 1,594
I thought it would be obvious, but I can't find a series representation of the Laplace transform. I'm looking for...
Nov29-12 08:48 AM
2 809
Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable,...
Nov27-12 05:43 PM
1 1,538
I have two 3d applications and when an object(a cube for example) is transferred between them, the rotation values of...
Nov28-12 08:06 AM
3 741
It's very difficult for me to find any simple literature to explain this idea. J\inMn(ℂ) is a coninvolutory (or a...
Nov29-12 01:42 PM
4 854
Hello, let's suppose I have two functions f,g\in L^2(\mathbb{R}) and I consider the inner product \left\langle f,g...
Nov29-12 06:54 PM
Stephen Tashi
7 1,282
Given two systems, Ax=b and Cy=d, for nxn matrices A and C, and n-dimensional vectors b and d, each of which has at...
Dec1-12 12:21 PM
1 831
The following problem was given on a test of mine and I got it completely wrong. If anyone can help me with solving...
Nov29-12 06:09 PM
1 689
After solving some problems about matrix invertibility and learning some theorems (and proving them), I have developed...
Dec1-12 01:22 PM
2 758
Hi guys I wonder if you know any linear algebra formalism or something to solve the following question...
Dec3-12 10:37 AM
3 945
I now know that inverses are only defined for square matrices. My question is: is this because inverses for non-square...
Dec2-12 06:57 AM
8 1,009
let A_i be an odd integer, s_i be the square of a_i and t_i be the triangular number, (s_i -1)/8. Same for a_j , s_j,...
Dec1-12 10:25 PM
2 1,260
At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this....
Dec2-12 12:37 PM
5 1,009
Bocard's problem asks to find the solutions to the Diophantine equation n!=m^2-1. The only known (n,m) pairs are...
Dec9-12 05:46 PM
3 1,590
I am trying to find a way to generate solutions to 5b^2*c^2 = 4a^2(b^2+c^2) Can anyone offer some insight? I...
Dec13-12 06:26 AM
55 6,635
the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer. find the least n s.t. f(n) is divisible by 17...
Dec5-12 09:33 AM
3 1,181
Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a...
Dec5-12 09:16 AM
1 1,602
Hi. There is a polynomial f = (x^3) + 2(x^2) + 1, f belongs to Q. It will be shown that the polynomial is irreducible...
Dec5-12 06:36 PM
1 687
I am curious about the proof of the fact that the value of a determinant computed using the Laplace (or cofactor)...
Dec6-12 12:09 PM
1 610
I need some help understanding the following definition: Definition: Let A\inMn(ℂ) the complex vector space ...
Dec8-12 09:11 PM
4 771
Hi Can anyone help with understand a basic idea, I have a matrix A in MATLAB which is 100x3000. I have checked...
Dec6-12 08:04 AM
2 654
If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with...
Dec9-12 09:35 PM
4 1,639
3.5036799918564934004113 I need help identifying this real number. The closest I have gotten is e+pi/4. But I...
Dec9-12 11:53 PM
9 1,819
I recall a post previously where the Op was wondering if any circle about the orgin having an irrational radius could...
Dec8-12 09:43 PM
4 1,253
I'm not a mathematician of any sort so excuse me if my question is stupid. I just realized that I could not define...
Dec10-12 10:52 PM
3 1,335
on page 261 of this paper by J. Vermeer ( he writes The...
Dec9-12 09:38 PM
4 748
Is anyone interested in learning some algebra? I was planning to go through Dummit and Foote (I have some basic group...
Dec9-12 01:56 AM
0 617
The proof goes as follows: For contradiction, assume there exists |s|< ∞ such that s = {e1, e2, ... , en} and...
Dec11-12 07:51 AM
1 528
Ok I promise this time it is not a homework type question. If someone could direct with a name of a theorem here,...
Dec12-12 08:54 PM
3 723
I've been reading a few mathematical definitions and I'm still not sure I grasp their significance. If Ax = b, then...
Dec13-12 04:42 AM
9 1,271
I'm still confused about L U matrix factorization. I'm trying to understand how to do it and why doing so is...
Dec11-12 03:00 PM
4 966
Hi All, I've been following a group theory course which I am struggling with at the moment. I'm from 3 different...
Dec11-12 07:36 AM
4 817
Hey! I am studying group theory for particle physicists right now and I came across the following general question...
Dec11-12 01:24 AM
0 571
So this is a pretty dumb question, but I'm just trying to understand homomorphisms of infinite cyclic groups. I...
Dec14-12 09:34 AM
10 1,116
I am not sure which rubric this belongs to, but since the zeta function is involved, I am putting it here. I noticed...
Dec12-12 11:15 PM
0 1,056
Can someone please explain to me, in as simple words as possible, what a quotient group is???? I hate my books...
Dec13-12 08:05 PM
2 676
A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find the bases and dimensions...
Dec14-12 01:21 AM
3 588

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