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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 35,137
is really the only way of checking which number is divisble by 7 is by modular arithematics?
Jan16-06 12:13 PM
12 2,448
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 2,390
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 2,820
i'm refering to this: does someone know if...
Apr4-06 01:15 PM
robert Ihnot
2 2,050
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 1,826
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 1,193
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 2,039
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 2,799
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 1,473
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 1,833
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 2,963
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 2,665
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 1,623
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 1,426
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 8,231
What is the rule of division by 23? Thanks in advance.
Jan24-09 04:57 AM
20 3,366
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 1,879
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 1,269
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 2,060
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 2,553
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 2,756
I found that the cartan subalgebra of ##sp(4,\mathbb{R})## is the algebra with diagonal matrices in...
Sep15-13 12:12 AM
4 958 Who discover that?
May3-11 02:58 PM
4 1,660
An Arithmetic Solution to the Goldbach Conjecture Prove that any and every even integer >4 may be expressed as the...
Oct6-11 01:50 AM
44 1,346
5x == 200 (mod 251) 11x == 192 (mod 401) 3x == -151 (mod 907)
Dec26-04 06:41 AM
matt grime
1 3,714
I can't figure this out no matter how many times I try. Please can someone help me with this homework question?: ...
Nov23-04 11:19 AM
3 1,043
I have almost no idea how to start! I'm just doing this problem for fun(or was at one time): Find all a such that...
Oct11-11 01:59 PM
Matt Benesi
10 3,288
Hello, I've been studying some linear algebra, and i am stuck on a certain definition. The book i am using says that...
Dec5-11 04:46 PM
4 794
I was recently thinking about these diophantine equations. I'm looking for solutions (x,y) in integers with d as an...
Dec6-11 05:51 AM
3 2,187
What exactly is gauss composition? I've heard of Manjul Bhargava's work, which apparently generalized gauss...
Dec19-11 09:09 AM
3 4,668
a and b are real numbers such that the sequence{c}n=1--->{infinity} defined by c_n=a^n-b^n contains only integers....
Jan23-12 04:58 PM
8 2,602
I was studying (yet another) number theory problem, described here: Prove that the equation x^3+y^3+z^3+t^3=1999...
Feb17-12 02:58 PM
24 3,606
Hello, I would like to see a solution to the following problem: Let A be a finite collection of natural numbers....
Apr27-12 11:23 AM
5 2,299
Hello, I wanted to know something regarding the quotient ring Z/pZ, where Z is the set of all polynomials with...
May4-12 01:05 PM
6 1,000
Hello, I was browsing a set of number theory problems, and I came across this one: "Prove that the equation...
Jun27-12 07:40 PM
7 1,693
I need help proving the following: 1 A non-square matrix cannot have both a left and a right inverse 2 If a...
Nov4-07 01:18 PM
2 9,556
How can I find the spectral decomposition of a linear operator on R^n, with a given matrix. Does anybody know a...
Dec15-08 09:42 PM
0 1,029
How do you write a matrix as a sum of a diagonalizable matrix and a nilpotent matrix? It would be great if you...
Dec17-08 07:47 AM
7 2,354
Hello everyone, I'm new to PF, so I hope this post is in the correct location. Anyway, does anyone know why one...
May22-11 11:28 AM
2 1,627
Hi, I was wondering why the latest theories about physics are about group theory and linear algebra. Maybe i don't...
Jun8-11 12:06 PM
0 447

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