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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 35,126
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
25 5,615
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
6 2,548
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
8 1,542
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
34 5,790
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
4 3,187
I've heard ppl say it is and it isn't, so is it a prime number? :P
Feb2-04 06:52 PM
3 2,625
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 2,369
scratch that. is 5606701775893 a prime number?
Jun1-11 09:10 PM
19 5,692
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
4 566
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
26 3,296
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 5,288
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
1 694
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
2 1,063
Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?
Aug5-09 09:06 PM
1 757
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
1 862
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
20 5,480
According to wikipedia, absorption is an axiom for a boolean algebra. This seems incorrect to me, since I believe...
Oct9-13 02:48 PM
3 789
Is an infinite series of random numbers possible? That is, can the term "random" apply to a infinite series? ...
May2-12 04:42 AM
89 13,299
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
7 8,161
Hi.. In the second paragraph of the following paper, there is a statement: "Because the direct product of subgroups...
Jun24-10 01:06 PM
1 1,714
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
5 1,404
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
4 749
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
2 564
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
2 2,811
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
6 4,459
IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q?? Attempt: Ive shown that this has no linear factors as +-1...
Aug18-08 03:18 AM
9 1,492
As an armchair theoretical physics fan, I recently ran across a tv program on the theory of fractual geometry as an...
Feb4-11 04:27 AM
10 2,223
Hi, I came across this article on Godel's incompletess theorem that seems to relate to number theory so I hope this...
Dec25-09 12:36 AM
12 4,729
Sorry I don't know how to write in symbols so I'm using Latex codes, anyway, the question is as in title: Is an...
Dec30-06 01:35 PM
matt grime
7 2,780
Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime. By coarsely...
Jan9-08 02:23 AM
23 6,701
Hello, I am begin billinear form and need help with a proof say you have an integral from 0 to 1...
Nov7-08 06:03 AM
4 1,414
Suppose that we've been given two polynomials and we want to find their Greatest Common Divisor. For integers, we have...
Jul13-12 12:38 PM
7 1,388
Hi, does anyone know why they call a ring a ring. Was it because of Z/(n), where the numbers sort of form a ring in...
Jun15-12 07:05 PM
1 862
Make a matrix G so that each element in G is another matrix with a constant dimension (i.e. 3 by 3). Hence a 3 by 3 G...
Sep17-06 02:59 AM
matt grime
10 1,686
Is it possible to write the 2010 numbers from 1 a 2010 in some order so that the 6933 digit number you get is prime?
Oct8-10 07:25 PM
11 1,653
I have heard about two or above dimensional plane which we can express R2 or Rn. But I never heard about...
Aug5-13 12:51 PM
1 597
In analogy to vector spaces, can we define a set of "basis functions" from which any continuous function can be...
Oct5-12 10:27 PM
7 1,772
Is it possible to extract the diagonal elements of a matrix into a vector USING ONLY MATRIX MULTIPLICATION? So no...
Dec15-11 02:06 PM
1 3,760
i.e. decimals of an irrational number, pi(n), etc. The function itself, f(n), can change with n, as long as it...
Aug22-08 08:56 PM
20 3,849
Denote Z_n=(0.1.2....n-1) Then could I generalize the number of homomorphism H:Z_n -> Z_m as gcd(n, m)=#(H:Z_n...
Feb17-11 11:19 PM
1 1,813

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