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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 35,094
I recall reading somewhere that Legendre's conjecture implies the Riemann Hypothesis. But the Wiki article suggests...
Jul27-09 11:58 PM
6 1,566
This subject came up in some notes on linear algebra I'm reading and I don't get it. Please help me understand. --...
Jul27-09 11:36 PM
7 1,130
I've been stuck on this for a while now, and I was wondering if anyone could help me out. The problem is: If...
Jul27-09 11:35 AM
16 3,142
Given positive integers a, b, c, d and for fractions a/b and c/d, it seems that ( a + c )/( b + d ) is between...
Jul27-09 11:18 AM
1 2,313
I am looking for two rotation matrices M1 and M2, which describe a rotation by an arbitrary angle around the axes...
Jul26-09 05:30 AM
4 1,427
A set of vectors V defines a Euclidean subspace. A subspace contains the zero vector. Now consider augmenting this...
Jul26-09 05:27 AM
2 814
Hi I have this question for my Linear Algebra class and I can't seem to figure it out. Let A and B be n x n...
Jul26-09 05:21 AM
2 4,474
Dear all, I have a question concerning Faugere's improved F4 algorithm. You can find it in the attached file ...
Jul25-09 11:56 AM
6 2,894
I've been trying to work out a bunch of problems that have to do with finding irreducible polynomials, and this one...
Jul25-09 09:25 AM
1 2,029
Hello. I wasn't sure whether to post this here on in some of the physics sections. I have a rank 2 tensor in one...
Jul25-09 08:12 AM
2 1,015
What is a good way to describe and count the Sylow 2-subgroups of S5? The ones isomorphic to D8 should be simple...
Jul25-09 02:14 AM
1 4,047
Will anyone help me to find out the analytic expression of the following 2^N\times2^N exponential? exp, where ...
Jul24-09 05:00 PM
0 1,191
So I came across this problem in my textbook, but couldn't seem to solve it... Let n be any squarefree integer...
Jul24-09 04:43 AM
1 1,127
I don't know if this has been posted already, but anwho... If you pick any positive integer greater than 9 and...
Jul23-09 05:38 PM
8 14,627
Other than the Riemann Zeta function, what equation has a non-trivial infinity of zeroes with real part one-half?
Jul23-09 04:55 PM
15 2,849
My work is on implicit FDTD method which allows time step (delta_t) above CFL limit. Implicit methods require one to...
Jul23-09 12:43 PM
0 839
A matrix is diagonalizable when algebraic and geometric multiplicities are equal. My professor proved this in class...
Jul23-09 03:59 AM
2 3,682
I have this problem where I'm having trouble solving so any help would be appreciated. Here's the problem: You...
Jul22-09 05:00 PM
2 2,067
(aT)∗ = \bar{a}T∗ for all a ∈ C and T ∈ L(V,W); This doesn't make much sense to me. Isn't a supposed to be=x+iy and...
Jul22-09 02:31 PM
3 1,044
is the following sequence finite \sum_{n=1}^{\infty} \frac{log^{u-1} (n)}{n} - u^{-1}log^{u}(n) if u=1 then we...
Jul22-09 06:57 AM
2 1,273
I'm a bit confused as to how to calculate the 2nd chebyshev function. I know \psi (x) = \sum_{p^k \le x} \ln p ...
Jul21-09 07:23 PM
1 1,300
Is anything more known about Legendre's conjecture that there is a prime between n^2 and (n+1)^2 for positive integers...
Jul21-09 01:50 PM
3 3,536
A matrix is diagonalizable when algebraic and geometric multiplicities are equal. I know this is true, and my...
Jul21-09 05:52 AM
2 1,390
I had this question on a test and I was wondering why it is false: If the row space equals teh column space then...
Jul20-09 06:48 PM
3 1,227
What is the geometric interpretation of unimodular matrices?
Jul20-09 03:42 PM
4 1,168
I have to prove that x*0= 0 where x is any integer. I can do this pretty easily using the proposition that m(-1)=-m...
Jul19-09 11:24 PM
3 3,053
Hello everyone, I have a query regarding the Gram-Schmidt factorization: Say I have 3 independent vectors, u, v,...
Jul19-09 04:52 PM
2 1,561
What is the basis for the vector space of all continuous functions?
Jul18-09 10:08 PM
John Creighto
15 1,983
Hi everyone, could someone please advise; The equation; PA - P atm A = K, change in X If I wish to factor...
Jul18-09 11:31 AM
Auto Engineer
4 1,471
Hello PF members This is my first post. It is rather complicated to understand but I request you to bear with me. ...
Jul17-09 04:48 PM
1 730
Hi All, this is not homework, just some basic revision for my own personal understanding, it's a long time since I...
Jul17-09 04:30 PM
Auto Engineer
2 783
In Linear Algebra and its Applications, David Griffel writes, "The components of covectors are often denoted by...
Jul16-09 10:42 AM
2 1,253
Hi, in the text I am reading I found the following implicit definition of an adjoint transformation: \overline{f}(...
Jul16-09 02:04 AM
4 2,909
Sorry, I have mistakenly posted it in the General Math forum. This was my fault. As I do not know how to correct...
Jul15-09 03:04 PM
0 1,573
I spend some time studying special functions recently. I found two definitions of gamma function, one in form of...
Jul15-09 11:37 AM
2 1,068
Given a 4x4 non-Hermitian matrix, is there any method I can use to prove the eigenvalues are real, aside from actually...
Jul15-09 08:51 AM
2 1,419
I need to find a way to sum/ a closed form representation for: \sum^{N}_{n=1}\frac{\Gamma(n-s)}{\Gamma(n+s)} ...
Jul15-09 01:13 AM
1 1,901
Hi. if anybody can help me Let S be the matrix a b c d with a constrain a =...
Jul14-09 12:23 PM
8 1,672
How would you write the following using index-notation? s \cdot F \cdot u Given that s = (s^0, \vec{s}) and u...
Jul14-09 09:32 AM
0 933
given the Selberg trace formula \sum_{n=0}^{\infty} h(r_n) = \frac{\mu(F)}{4 \pi } \int_{-\infty}^{\infty} r \,...
Jul14-09 07:35 AM
0 1,263

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