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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 35,867
Hello Everyone. In a thread in this forum relating to a problem on Subspaces I read that as long as a Vector...
Jul1-07 07:12 PM
8 3,696
Is there any difference between a vector subspace and a linear manifold. Paul Halmos in Finite Dimensional Vector...
Oct31-08 06:57 AM
13 8,612
Hello all. I came across this problem in Halmos, Finite-Dimensional Vector Spaces, page 16. Is the set R of all...
Apr5-08 01:41 PM
33 11,868
Hello all I have read about quotient spaces of a vector space in several books and have an understanding of what...
Mar30-08 08:22 PM
2 1,417
In several places I have come across what seems to be a standard proof by contradiction that there is no greatest...
Dec6-09 09:50 AM
14 6,422
Howdy, I just stumbled on this forum and was hoping someone could help with this proof: If a and b are elements of...
Dec12-04 11:27 PM
3 1,636
in this webpage there is a book about recreational maths in it there is a paradox by raymond smullyan, it's on page...
Nov2-03 08:34 AM
11 2,656
i read the book "the man who loved only numbers" by paul hoffman, and there is explanation about fermat's test for...
Nov1-03 12:35 PM
8 3,381
can some one explain to me how is taking the logarithm of euler product gives you -sum(p)+log(s-1)=log? my question...
Dec18-03 12:28 PM
2 3,912
i think everyone is familiar to this but i wonder if someone has made his research to study it. what i mean is the...
Feb19-04 07:41 AM
12 2,326
im not trying to be a crank and give you a solution to it but im looking for the proof of Ivan Vinogradov "that every...
Mar2-04 09:07 AM
7 4,498
i made a question by myself here it goes: proove that the only solution to p is 3: n^2-1=p where n is a natural...
Mar25-04 09:34 AM
matt grime
5 1,782
in mathworld, they say that conway proved "that Collatz-type problems can be formally undecidable." does it mean that...
Jan4-05 11:07 AM
14 3,550
is really the only way of checking which number is divisble by 7 is by modular arithematics?
Jan16-06 12:13 PM
12 2,462
i reackon youv'e seen it already, the problem is to rearrange the next numbers in the fixed order: 1 2 3 4 5 6 ...
Jan29-06 12:09 AM
3 2,399
is there some theorem of some sort, that connect the number of divisors of a number to identify if it's even or odd? ...
Apr2-06 12:47 PM
4 2,827
i'm refering to this: does someone know if...
Apr4-06 01:15 PM
robert Ihnot
2 2,067
i chekced a few perfect numbers with module 6 and, a nice property is that all mod 6 equal 4 (at least for those i...
May7-06 06:04 AM
9 1,850
i need to remember when does Ax=B has a unique solution, more than one, and no solution? i think that it has a...
Jun14-06 02:48 AM
1 1,203
i need to find how many automorphisms are there for the field Q(sqrt2). i am given the hint to use the fact that a is...
Nov30-06 12:10 PM
8 2,057
let V be a vector space and K a nonempty subset of V prove/disprove : K is linear independent set iff for every T...
Feb5-07 07:01 AM
11 2,821
i need to prove diprove that there exist matrices A1,A2,...,As such that rank Ai=1 for every i=1,...,s and...
Feb5-07 08:20 AM
2 1,477
1) there's given a transformation f:C^n->C^n (C is the complex field), it's known that f is linear on R (real numbers)...
Feb5-07 04:54 PM
matt grime
5 1,845
the question is as follows: gcd(n,10)=1, i need to prove that there exists a k>=1 such that 10^k-1 is divisible by n....
May4-07 01:36 PM
15 2,997
i have this matrix: 011 001 000 and i need to find the matrix jordan basis, and jordan form. for the jordan...
May4-07 03:45 AM
10 2,674
im given a matrix H from M_n(C) (the space of nxn matrices above the comples field). and we know that for every a in...
Jul10-07 08:55 AM
matt grime
8 1,648
There's a question that asks me to show that there exists a unique linear transformation from: f\otimes g: V_1\otimes...
Jul5-08 02:47 PM
9 1,436
I know how the rotation matrix looks like in the 2x2 and 3x3 orders, but how does it look in general? thanks in...
Aug1-08 02:56 AM
9 8,261
What is the rule of division by 23? Thanks in advance.
Jan24-09 04:57 AM
20 3,384
Is there a formula to compute how many inversions are there in a given permutation?
Feb21-09 10:31 PM
0 860
Perhaps someone will help me in this. I need to prove that the group of elements of the form gh g^{-1}h^{-1} where...
Mar7-09 06:25 AM
2 969
What fields of interest in number theory should I learn to fully understand his and Taylor's proof? Is there a...
Mar25-09 01:31 AM
matt grime
5 2,368
Does someone know if there's a course offered on RH? I mean reading the literature can be quite intimidating...
Aug9-10 09:44 PM
5 2,019
Can someone give me a hint how to show the recurrence relations for G_k(z) ,in wiki it's for the d_n's? Other than...
Mar5-11 10:58 PM
3 1,891
I want to show that if 1 were a congruent number then there would be an integer solution to the equation x^4-y^4=u^2...
Mar20-11 09:03 AM
3 1,286
I am asked to find all the modular forms with weight k which don't have zeros on the upper half plane. I know that...
Mar27-11 07:13 PM
Stephen Tashi
4 2,080
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 2,579
From taking breaks from preparing for a talk I have in geometry, I started toying a little bit with perfect numbers. ...
Sep1-12 03:31 PM
10 2,787
I found that the cartan subalgebra of ##sp(4,\mathbb{R})## is the algebra with diagonal matrices in...
Sep15-13 12:12 AM
4 980 Who discover that?
May3-11 02:58 PM
4 1,676

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