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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
1 30,452
I have been long thinking on how one would set up an integral to find the area under a helix (the area between the...
Aug2-11 06:07 AM
8 8,039
I'm going through the proof of Cauchy's Theorem in a text book and I'm stuck on a particular point. I've tried looking...
Aug4-11 02:59 AM
4 3,433
THE PROOF THAT AN ODD PERFECT NUMBER DOES NOT EXIST Let us firstly suppose that such an odd number (X) member of...
Aug2-11 03:04 AM
6 7,223
Can anyone please explain the largeness of Graham's number? I tried looking it up in google, but didn't quite...
Aug9-11 02:05 AM
5 6,399
Esteemed Algebraists: Please help me understand better the definition of a transvection. Let V be a...
Jul28-11 10:28 PM
3 1,646
Hi, I have a rotated frame (new matrix, T(x,y, z)) and the original frame (old matrix T(X,Y,Z)). I want to use this...
Aug4-11 02:11 PM
3 2,691
It's pretty wierd....but i don't understand that why the dot product of two vector quantities is a scalar quantity and...
Aug5-11 05:41 PM
7 2,614
if A is a square matrix Ax = 0 has exactly one solution if and only if Ax = b has at least one solution for every...
Jul28-11 07:26 PM
2 2,887
My background in linear algebra is pretty basic: high school math and a first year course about matrix math. Now I'm...
Aug6-11 11:25 AM
32 7,949
Let A be an n x p matrix with real entries and A' be its transpose. Is the column space of A'*A the same as the column...
Jul29-11 05:14 PM
1 1,549
gcd and lcm ( 1 2 3 ... Last)
Hi, I encountered the following formula while reading, can anyone prove this: lcm(a,b)=gcd(a^{-1},b^{-1})^{-1} ...
Jul30-11 07:38 AM
59 8,263
I defined the angle \theta between x \in \mathbb{R}^k and y \in \mathbb{R}^k in the way that: \theta = \cos...
Aug3-11 10:19 PM
1 1,116
As we know for the average Undergrad attempting to grasp (and understand) these abstract mathematical concepts can be...
Jul29-11 09:18 AM
1 1,753
Say I have 2 complex (normalized) column vectors x and y in C^N: The standard dot product <x,y> = x*y (where *...
Jul29-11 09:10 AM
1 917
Hello, if B is a positive semi definite matrix, how can you complete the square around B from x'Bx + x'Cy +...
Jul29-11 10:39 AM
1 2,744
I've been doing some work and I keep running into polynomials of the following form: P(x,y,z) = ax^2 + by^2 + cz^2...
Jul31-11 02:56 PM
Citan Uzuki
9 2,473
I'm trying to create a circle in 3D based off of 4 inputs. Position1 Position2 LineLength1 LineLength2 The...
Jul30-11 10:36 PM
I like Serena
14 1,688
Is the following theorem true: Theorem: Suppose a, \, b \in \mathbb{R}^k. If |a| + |b| = |a + b| , then |a| and ...
Aug4-11 10:53 PM
3 1,604
I'm studying the S_n groups and I've been calculating a bunch of compositions of m-cycles. I haven't, however, been...
Aug5-11 09:49 AM
Stephen Tashi
1 1,769
I am trying to understand the notions of rank of an R-Module, free-module, basis, etc. I would like to understand...
Jul30-11 06:50 PM
6 2,135
Hello, I just took ordinary diff eq and I've had calc III and linear algebra, but I'm worried about taking Modern...
Aug2-11 10:33 PM
9 2,969
I think this is a pretty simple question. I need a transformation that will take a Column vector e.g.: <a,b,c> and...
Aug4-11 10:35 PM
3 1,967
Hello, If I have block matrices A,B,C and D all of which are non singular would this relationship hold; my main...
Aug1-11 03:13 PM
2 1,509
A natural integer N can be written as x mod p, for instance: N... 1 2 3 4 5 6 7 8 9 10 11 12 p=2 1...
Aug2-11 01:37 AM
0 1,572
I am learning about tensors. Is gαβAβ the same as Aβgαβ ? Thanks for any help.
Aug4-11 07:36 AM
10 1,399
Hello, I'm wondering if this is true, or if anyone has seen this before: Let q, t be coprime integers. Then...
Aug4-11 04:20 AM
2 2,831
Hi, All: Please forgive my ignorance here: let G be an infinite group, and let H be a subgroup of G of finite...
Aug6-11 03:53 PM
8 2,785
Hi, my problem is simple enough to write down but (to me) seems quite difficult to solve. My equation is as follows...
Aug5-11 10:50 AM
1 1,513
Hi, I have two diagonal matrixes (rotated and origin), how can I calculate the rotation matrix between these two...
Aug3-11 07:15 PM
0 1,277
hello, I'm examinating the theorem of power series, specially taylor series I know a function f(x) can be written...
Aug4-11 04:41 AM
2 832
I have enrolled for a distance learning progaramme from IGNOU(big mistake!).There is a paper on linear algebra.The...
Aug5-11 08:38 PM
11 3,308
Hi, I'm new to linear algebra. I'm pretty good at doing exercises with matrices and stuff but even though I've been...
Aug10-11 01:12 AM
6 3,118
Hi, as no unique unique analytical solution exists to my problem (as another poster pointed out), I have taken to...
Aug8-11 12:49 PM
8 1,957
In an integral domain, I found that the number of maximal ideals in a Notherian ring containing a particular element...
Aug6-11 05:07 AM
2 1,182
Let R be a commutative ring with 1. If there exists a non-zero R-module M such that every submodule of M is free, then...
Aug9-11 10:42 PM
6 1,985
Hi. I have a few simple questions. (<- sorry, please click this image.) 1. What does the notation in the red...
Aug7-11 08:31 PM
2 2,375
I have read that we do not know if there are an infinite number of Fibonacci primes. So far, no one has produced a...
Aug9-11 03:47 PM
6 3,051
I'm trying to make sense of two different definitions of an algebra over a ring. The definitions are as follows: If...
Aug9-11 12:32 PM
7 1,385
I have a matrix D (it happens to be in R^(nxm) where n>>m, but I don't think that is relevant at this point). I also...
Aug8-11 07:20 PM
I like Serena
1 1,739
Just a quick question. What areas of mathematics would I have to study to understand Wiles' proof? I know his proof...
Aug9-11 09:24 AM
1 2,021

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