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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 35,947
im teeching algebra and had to prove that X^5 - 8 was irreducible over the rationals. so i did it using eisenstein. ...
Apr20-06 06:50 PM
mathwonk
4 4,069
Can someone explain to me why the following is true (ie, show me the proof, or at least give me a link to one): ...
Aug22-08 05:01 AM
sd522527
15 10,874
Hi, yet another question regarding polynomials :). Just curious about this. Let f(x), g(x) be irreducible...
Jun15-11 08:21 PM
burritoloco
5 1,409
Is it true that polynomials of the form : f_n= x^n+x^{n-1}+\cdots+x^{k+1}+ax^k+ax^{k-1}+\cdots+a where...
Nov26-11 08:32 AM
COURAGE_WOLF
5 1,973
I am attempting to construct a field containing 625 elements and should be in the form Zn mod f(x). Factoring 625...
Nov9-07 03:09 AM
matt grime
1 4,773
okay so i was reading a book on representations and found this discussion and was confused:...
Jan22-10 08:29 AM
wofsy
3 4,920
Hi guys, I have a question which is very fundamental to representation theory. What I am wondering is that whether a...
Jul24-10 06:35 PM
nematic
0 1,655
All commutative groups have one dimensional representation ##D(g_i)=1, \forall i## I understand what is...
Jan10-14 08:40 AM
Office_Shredder
14 1,101
So I'm studying molecules and symmetry and I was wondering if there was a intuitive way of understanding why there are...
Oct16-10 10:34 AM
sineontheline
1 1,053
Does anyone know how to classify the finite-dimensional irreducible representations of so(4,C)? Can they all be built...
Aug6-09 05:08 PM
aziz113
2 2,879
Hi all, The representations S^1 = \mathbb{R}/\mathbb{Z} \to U(1) are of the form \rho_n : \mapsto e^{2\pi i n x}...
Feb2-08 11:08 PM
jdstokes
1 1,639
Proposition. A polynomial of degree 2 or 3 over a field F is reducible iff it has a root in F. Tell me if I'm on...
Nov18-09 05:51 AM
HallsofIvy
1 760
If you were to tell me that "range" and "span" meant the same thing I would understand why, in english their meaning's...
May22-12 07:58 PM
alexfloo
29 2,999
I'm really confused... we refer to the "size" of a group as the "order"... But are they really equivalent? Can we...
Oct31-12 06:39 PM
micromass
2 884
In set theory, we may define a function A --> B to be a relation on AxB that is "single valued": to each a in A there...
Sep22-09 08:21 AM
Hurkyl
0 734
We all know the definition of prime numbers and the first prime number is always 2. Why is -1 not listed as a prime...
Jul23-05 01:53 PM
Hurkyl
25 5,717
Hi, not sure if this is the right forum.. pls move if not. Almost 30 years ago, I was studying engineering and my...
Nov18-11 05:54 PM
narrator
6 2,601
Am I missing something or is 0 a prime element in an integral domain? In the definition of prime element p of an...
Feb28-08 10:17 PM
mathwonk
8 1,553
Hi there, this is my first post here so I'm sorry if this is in the wrong place, asked before, standard newbie...
Oct20-11 06:12 PM
D H
34 5,924
At first, when I saw this, I was deeply shocked and lost the believe that math is absolute. Like the thinking that if...
Jan16-09 04:59 PM
HallsofIvy
4 3,214
I've heard ppl say it is and it isn't, so is it a prime number? :P
Feb2-04 06:52 PM
mathman
3 2,643
Can some one tell me how to figure out if this is solvable or not? For the Prime number p=68659, 19=x^2 mod p. ...
Dec11-07 02:11 PM
robert Ihnot
12 2,412
scratch that. is 5606701775893 a prime number?
Jun1-11 09:10 PM
ramsey2879
19 5,720
Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group...
Jul24-13 07:13 PM
micromass
4 590
Hi, I'm not sure if this is the right section, but I'm talking about numbers :). The questions is as written in...
Oct25-11 02:48 PM
lavinia
26 3,372
I was reading Lie Algebras in Physics by Georgi.......................second edition... Theorem 1.2: He proves that...
Dec24-09 03:15 AM
krishna mohan
3 5,356
I don't know how to write out matrices nicely on this forum, but suppose you have some matrices: This...
Nov5-12 01:54 PM
micromass
1 702
I've been working on this Linear Algebra problem for a while: Let F be a field, V a vector space over F with basis...
May26-12 11:23 AM
imurme8
2 1,079
Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?
Aug5-09 09:06 PM
D H
1 763
If V is a vectorspace and v is a vector in V. will the projection of v onto V be v?
May7-12 03:34 PM
tiny-tim
1 873
A vector space is a collection of vectors. So can we say that it is a set (although with special properties) ? Just...
Jan22-11 12:37 PM
sponsoredwalk
20 5,561
According to wikipedia, absorption is an axiom for a boolean algebra. This seems incorrect to me, since I believe...
Oct9-13 02:48 PM
mfb
3 836
Is an infinite series of random numbers possible? That is, can the term "random" apply to a infinite series? ...
May2-12 04:42 AM
micromass
89 13,502
Hello, If f is a morphism between two vector spaces, we say it is linear if we have: 1) f(x+y) = f(x) + f(y) 2)...
Dec8-09 06:20 PM
DrGreg
7 8,285
Hi.. In the second paragraph of the following paper, there is a statement: "Because the direct product of subgroups...
Jun24-10 01:06 PM
Landau
1 1,735
hi there. I have an equation i derived from a "belt problem" (i actually dont know if it's correctly derived yet)....
Apr8-10 09:26 PM
Live2Learn
5 1,417
I came across this statement but I am not so sure. I was stuck on this counter-example \begin{pmatrix} 0&1\\0&0...
Feb13-13 01:34 AM
CompuChip
4 766
I am a bit confused, so this question may not make much sense. A unitary operator from one vector space to another...
Feb22-14 04:59 PM
D H
2 590
Hi Given a square matrix R_{X} that is Toeplitz, is it necessarily invertible? I am not convinced about this. ...
Nov15-08 08:39 AM
maverick280857
2 2,835
questions: why is the sum of all the roots of unity equal to zero? z^(1/n)=z1,z2,...zn z1+z2+...+zn=0 It's...
Jan11-09 03:57 AM
dodo
6 4,509

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