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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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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 34,268
Hello, while dealing with non-homogeneous equations with constant coefficients I met a following problem. I need an...
Aug22-11 09:04 AM
4 2,020
In one of my tutorial problems, I was asked to verify if the following function is a valid inner product <x,y>=...
Aug21-11 03:58 PM
5 2,503
Rational numbers are those that can be represented as a/b. It is simple (I think) to demonstrate that the series of...
Aug21-11 01:59 PM
124 19,092
Hi guys, I just need to know if Goldbach's Conjecture has been demonstrated or not! Thx! :D
Aug21-11 05:04 AM
38 11,387
In my lecture notes, the lecturer describes the column space of matrix A as the vector space spanned by the columns...
Aug20-11 05:58 PM
3 1,229
For discrete groups, we can easily find the decomposition of the direct product of irreducible representations with...
Aug20-11 03:34 AM
8 2,794
Some confusion here reviewing some algebra. From what I remember, a homomorphism must be specified in order to...
Aug19-11 08:01 PM
5 2,486
Hi, here's the problem: for m = {{a, b}, {c, d}}, m \cdot m is suppose to = {{a^2 + b c, a b + b d}, {a c + c d,...
Aug19-11 07:51 PM
6 2,919
I took an Intermediate Linear Algebra course all last year (two semesters worth) and we covered the CDT. My professor...
Aug19-11 05:10 PM
3 2,464
If we want to caculate the projection of a single vector, v=(1,2) (which is an element of an R2 vector space called V)...
Aug19-11 03:47 PM
2 1,341
Dear Friends, I'm would like know classic problems about parity property, in other hand, classic problems...
Aug19-11 06:13 AM
2 2,455
Hello matrices masters, If A and B are nxn square matrices, is there an identity for the determinant of the block...
Aug19-11 04:56 AM
4 1,856
Just a small question, I think I may have missed this part out in our lectures or something. :| Suppose I have a...
Aug18-11 02:55 PM
I like Serena
2 1,296
Sylow's theorem tells us that there is one 7-Sylow subgroup and either one of seven 3-Sylow subgroups. Call these...
Aug18-11 12:14 PM
2 1,323
I'm interested in analytic number theory and from what little I understand of it complex analysis will be more...
Aug18-11 11:33 AM
2 2,714
Hi. see the image. In the integral there's no dx,dy,dz thing. Does this make any sense? Isn't it errata?
Aug18-11 01:09 AM
5 1,466
It is well known that the Harmonic Series diverges (1/1+1/2+1/3+1/4+...), but that the series converges. In the...
Aug17-11 09:48 PM
3 2,192
My theorem is right. "Inside a regular inscribed hexagon, the radius of the circle IS equal to the sides of the...
Aug17-11 11:08 AM
Vanadium 50
5 1,377
I'm trying to do something that requires solving an eigenvalue problem of the form A_{imkl} c_m c_k c^*_l=\lambda c_i...
Aug17-11 08:37 AM
1 1,385
Hi everyone, This is not a homework question. Let B_1 and B_2 be orthonormal bases. Let M be the change of...
Aug17-11 02:59 AM
0 2,000
Hi, I understand the fact that grp theory textbooks defined Hom(G, H) as (g + h) u forms a group homomorphism. I...
Aug17-11 02:20 AM
4 2,061
i am sorry guys, the last time i posted this problem it was completely different but this time if we Let x12+x22=1 be...
Aug16-11 03:39 PM
4 5,162
I'm not sure it's safe to post real theorems here. Is it?
Aug16-11 02:47 AM
57 6,437
Let (N, s(n), 0) be a Peano space. That is, N=\{1,2,3,\dots \} is a set in which Peano arithmetic can be used. We...
Aug15-11 12:04 PM
4 3,014
In school I've always learned that tensor transformations took the form of: \mathbf{Q'}=\mathbf{M} \times...
Aug15-11 11:40 AM
4 2,394
Hi , I was trying to understand why or where would the problem arise in the definition of the direct sum for the...
Aug15-11 02:24 AM
1 1,632
Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt + b = 0 are not identically? How can I expand the second...
Aug14-11 11:59 PM
2 1,405
To prove that : f : U_{s} (st) \rightarrow U(t) is an onto map. Note that Us(st)= {x \in U(st): x= 1 (mod s)}...
Aug14-11 09:20 PM
5 2,155
The sequence is 1,2,3,4,5,8,7,16,9 I am absolutely stumped and cannot fathom the answer. Normally I can see the...
Aug14-11 08:06 AM
1 3,154
let C0 be the set of continuous functions f : R -> R. For n >= 1, let Cn denote theset of functions f : R -> R such...
Aug13-11 01:23 PM
4 1,866
Is there shortcut methods for the solution of simultaneous equations when the given matrix is of order 4 and above? A...
Aug13-11 08:04 AM
4 3,091
Hi, I have a problem that I'm a bit stuck on, and need some direction: I need to find \forall_n within a...
Aug13-11 03:35 AM
15 6,495
I know that a set (let's call it V) of all functions which map (R -> R) is a vector space under the usual...
Aug13-11 12:46 AM
5 2,394
Can we describe describe n such that Z_n has exactly 12 invertible elements? Thank you
Aug13-11 12:24 AM
13 3,870
Why is every matrix (complex) similar to its transpose? I am looking at a typical jordan block and I see that the...
Aug12-11 09:17 PM
2 3,157
I was taking a lecture series this summer at my school where a professor was introducing us to introductory Galois...
Aug12-11 12:20 PM
2 2,069
Q)Different eigenvectors corresponding to an eigenvalue of a matrix must be linearly dependant? Is the above...
Aug12-11 08:35 AM
2 1,949
Hi, All: Given a quadratic form Q(x,y) over a field of characteristic different from 2, we can find the...
Aug12-11 12:14 AM
3 2,208
I'm looking for a general-case method to find at least one solution to a system such as a_0 = a_1*x_1 + ... +...
Aug11-11 05:08 PM
4 1,258
Hello all. This is my first post here. Hope someone can help. Thank you guys in advance. Here is the question: I...
Aug11-11 01:53 PM
2 2,562

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