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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
micromass
1 34,761
What is positive and negative eigenspaces? Can you recommend me a referance to know them?
Aug23-11 01:18 PM
quasar987
2 1,988
Suppose that there is an integer n>1, such that an=a for all elements of some ring. If m is a positive integer and...
Aug23-11 12:43 PM
tiny-tim
1 979
I found in page 225 of this article http://www.dm.unito.it/~cerruti/ac/schoof-counting.pdf that the endomorphism...
Aug23-11 09:13 AM
yavanna
0 1,691
Hey, this is my first post, so... Hello everybody! I've been looking into the Collatz conjecture, and like most...
Aug22-11 05:13 PM
prdgi
2 2,809
I have a quick question regarding matrix equations. Usually, I would look this up but unfortunately I'm away from the...
Aug22-11 09:46 AM
micromass
8 1,240
Hello, while dealing with non-homogeneous equations with constant coefficients I met a following problem. I need an...
Aug22-11 09:04 AM
jambaugh
4 2,027
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
HallsofIvy
5 2,505
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
Bourbaki1123
124 19,118
Hi guys, I just need to know if Goldbach's Conjecture has been demonstrated or not! Thx! :D
Aug21-11 05:04 AM
johnny_boy
38 11,400
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
micromass
3 1,230
For discrete groups, we can easily find the decomposition of the direct product of irreducible representations with...
Aug20-11 03:34 AM
Simon_Tyler
8 2,796
Some confusion here reviewing some algebra. From what I remember, a homomorphism must be specified in order to...
Aug19-11 08:01 PM
micromass
5 2,491
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
nigels
6 2,921
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
Kindayr
3 2,471
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
JamesGoh
2 1,347
Dear Friends, I'm would like know classic problems about parity property, in other hand, classic problems...
Aug19-11 06:13 AM
nulll
2 2,458
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
daveyp225
4 1,858
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 1,298
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
Samuelb88
2 1,325
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
mathwonk
2 2,718
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
daveyp225
5 1,468
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
micromass
3 2,195
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 1,379
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
Manchot
1 1,386
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
CantorSet
0 2,004
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
daveyp225
4 2,070
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
dodo
4 5,164
I'm not sure it's safe to post real theorems here. Is it?
Aug16-11 02:47 AM
D H
57 6,444
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
Kindayr
4 3,022
In school I've always learned that tensor transformations took the form of: \mathbf{Q'}=\mathbf{M} \times...
Aug15-11 11:40 AM
aeson25
4 2,397
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
Sumanta
1 1,633
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
crocque
2 1,409
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
daveyp225
5 2,157
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
agentredlum
1 3,157
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
Fredrik
4 1,871
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
gb7nash
4 3,093
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
RamaWolf
15 6,504
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
SteveL27
5 2,399
Can we describe describe n such that Z_n has exactly 12 invertible elements? Thank you
Aug13-11 12:24 AM
arthurhenry
13 3,880
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
arthurhenry
2 3,160

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