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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 30,475
Hi, I need help with simply starting to prove this. I'm terrible with proofs and even the easy ones are hard for me....
Jul19-11 07:01 PM
1 2,708
I recently got interested in number theory and have been fiddling around with Scilab trying to find interesting...
Jul17-11 02:37 AM
8 4,746
Hi, Quick question here: I know that C-S inequality in general states that |<x,y>| \leq \sqrt{<x,x>} \cdot...
Jul13-11 07:57 AM
8 1,718
Hello, I'm wondering if there's some nice formula for the expansion of trinomials, like this: \prod_i \left(y +...
Jul15-11 07:04 PM
2 1,862
I know you can decompose GL(3,R) into SO(3) x Diag x SO(3), but i was wondering if you could generalise this to a set...
Jul13-11 07:09 AM
0 1,007
I have a matrix of the form X = , where A and B are matrices of equal dimensions (M x N). I am looking for an elegant...
Jul15-11 05:32 PM
11 2,326
I am trying to take the derivative of an inner product (in the most general sense over L^2), and was curious if...
Jul13-11 06:17 AM
1 2,762
Hey all, I was hoping someone could explain to me how to calculate the angle between matrices, ie. two square...
Jul17-11 08:36 AM
4 3,820
I'm trying to learn linear algebra using Schaum's outline and this is one of the practice problems: Find and...
Jul13-11 02:19 PM
3 1,301
I'm reading up on the classification of finitely generated modules over principal ideal domains. In doing so, I...
Jul24-11 08:50 AM
10 2,837
I have observed a strange thing when you modify a sequence of numbers bit by bit.
Jul20-11 07:08 PM
2 2,512
Hello. I'm quoting Bertsimas, D., and J. Tsitsiklis, Introduction to Linear Optimization: "For the purposes of this...
Jul14-11 05:46 PM
0 1,191
I forgot why the next statement is true and it's bugging me endlessly... If p is prime such that p =1 mod 4 then...
Jul23-11 06:36 AM
4 2,436
So if G = Q8 = <a, b : a^4 = 1, b^2 = a^2, b^{-1}ab = a^{-1}> I'm fine with the notion of the derived subgroup G' =...
Jul16-11 07:53 PM
1 1,751
I'm looking for the title to a popular introductory book on graph theory. For the best possible recommendation,...
Jul20-11 12:02 PM
3 1,693
I have n elements. Say n = 3. Suppose I have an association matrix that gives the relationship between each...
Jul24-11 03:32 AM
1 1,279
Ok, so the title didn't allow me to be too descriptive. Basically, I'm trying to formulate a variant of the time...
Jul18-11 10:05 AM
1 2,077
I am trying to ultimately find the projector onto a convex set defined in a non-explicit way, for a seismic processing...
Jul18-11 02:02 PM
2 766
Lemma. A group G of order 6 can have only one element of order 3. Pf. Suppose G has two elements of order 3. Call...
Jul18-11 08:22 PM
12 977
Why is it not possible for a filed to have have two prime fileds one isomorphic to Zp and the other isomorphic to Zq ...
Jul19-11 03:11 AM
1 795
For a dimension 1 regular semi-local ring, does the Picard group vanish? What if it is not regular? (and what if I...
Jul19-11 09:40 AM
2 1,342
Is there an "easy" method to finding subgroups of finitely generated abelian groups using the First Isomorphism...
Jul19-11 12:16 PM
1 1,226
I do not know if this is a common/standard construction, so here is my motivation for this question. From Crystal...
Jul21-11 09:06 AM
2 1,656
I am a physicist, so my apologies if haven't framed the question in the proper mathematical sense. Matrices are...
Jul21-11 06:17 AM
5 1,435
Why is the transpose of a matrix important? To find the inverse by cofactors we need the transpose but I would never...
Jul21-11 08:45 AM
2 1,290
Hi, I'm pretty rusty with solving linear equations, my equations are: ai = bijkcjk i = 1,... n j, k = 1,......
Jul22-11 12:01 PM
Ben Niehoff
6 2,156
Brocard's problem asks to find integer values of n for which n! + 1 =m^2 . where n! is the factorial.Probably I got...
Jul25-11 09:17 AM
3 2,935
Find the sum of : ^{}0/3] + ^{}1/3] + ^{}2/3] + ^{}3/3] + ^{}4/3] + .... + ^{}2008/3] where is the greatest...
Jul25-11 01:56 AM
18 3,642
Given matrices in a vectorspace, how do you go about determining if they are independent or not? Since elements in...
Jul22-11 03:56 PM
2 1,762
I'm stuck on a problem which asks: Determine whether W is a subspace of R^3. If W is a subspace, then give geometric...
Jul22-11 04:05 PM
1 1,190
Wikipedia states: when G splits as direct sum of H and K, then Aut(H \oplus K) \cong Aut(H) \oplus Aut(K) ...
Jul23-11 08:36 PM
5 938
In the context of matrices and linear algebra, what is the general solution ? Is it the value of the variables that...
Jul23-11 02:49 AM
0 973
I can't for the life of me understand this topic. given a point x =(1,1,1,1,1,1,1) and a primal LP, does the point...
Jul25-11 03:20 PM
2 1,678
I am examining the conjugacy classes of S_5. I know that two elements in S_5 are conjugate if and only if they have...
Jul25-11 07:07 PM
1 1,788
I'm reading from Wikipedia: I thought linear operators always had eigenvalues, since you could always form a...
Jul26-11 10:55 PM
9 1,898
The book I use for linear algebra explains that the motivation for defining a vector space has to do with the Gauss'...
Jul27-11 04:01 AM
3 1,844
Hello, Say we have field (F,+,.) and field extension (E,+,.), then the degree of the field extension (i.e. the...
Jul26-11 08:46 PM
3 1,995
In many areas (say, electrodynamics) we come across expansions of any function in terms of a series of orthonormal...
Jul26-11 06:02 PM
0 964
By F I mean the polynomials with coefficients in field F. By F(X) I mean the rational polynomials. I have a feeling...
Jul27-11 12:16 PM
10 2,096
Hello, After a theorem stating that the product, sum, etc of two elements of a field extension that are algebraic...
Jul27-11 05:55 PM
3 2,062

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