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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 33,911
What is the infinite product for the function \Xi(s)=\Gamma\left(\frac{s}{2}\right)\pi^{-s/2}\zeta(s) ?
Feb17-10 07:52 PM
3 3,395
Here is an interesting problem that I've been thinking about for a while: Let p be a prime s.t. p = 4m+1 for some...
Feb1-10 10:12 AM
3 3,834
Hello. I have been reading a book with an introductory section on number theory and the part regarding Euler's...
Jan22-10 12:22 PM
3 2,500
From this example Anti-Aliasing section 22.4.1
Jan26-10 10:56 AM
3 1,783
Hi Folks, I have a question about determinants that is probably quite simple. I know that if you have a matrix and...
Jan27-10 09:32 AM
3 967
I wonder if all coupling set of equations are not solvable analytically? I have a equation set as follows y1 =...
Jan27-10 12:07 PM
3 1,264
Hello dear forum member I wanted to know how about the research on this branch of science.Are many people working on...
Jan31-10 06:06 AM
3 2,181
Hi, I have just started teaching linear algebra to myself. I know nothing about linear algebra so if this question...
Feb3-10 06:50 PM
3 2,947
Hey everyone, I'm taking this course called "Number Theory" and am having a lot of difficulty with it. We're...
Feb2-10 10:38 PM
3 1,656
Hi, I am new with linear algebra, and I'm having a hard time wrapping my mind around the 0 vector and the additive...
Feb2-10 07:40 AM
3 1,858
I recently teach myself linear algebra with Friedberg's textbook. And I have a question about adjoint operator, which...
Feb4-10 06:04 AM
3 1,154
hi. i'm reading "quantum mechanics in hilbert space" and a don't get a basic point for bounded operators. def. 1...
Feb10-10 07:25 AM
3 933
Clearly I am missing something obvious here, but how is it that negative even numbers are zeros of the Riemann zeta...
Feb10-10 12:10 PM
3 4,524
Hello math goers, My education in linear algebra is limited to an Intro course I took a year ago. So I am posting...
Apr12-10 05:34 PM
3 1,165
G group, H subgroup of G. Suppose aH and bH are distinct leftcosets then Ha and Hb must be distinct right cosets? ...
Feb16-10 08:25 PM
3 2,771
"Let m and k be positive integers and φ(m) is the Euler's phi function. Then the number of integers n such that 1≤n≤mk...
Feb21-10 04:31 PM
3 1,634
I'm a physics major. As such, I have come across several situations in my studies that require the use of eigenvectors...
Feb22-10 09:04 AM
3 1,793
4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be...
Feb22-10 05:20 PM
3 1,841
I am having trouble understanding this example: Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are ...
Feb25-10 02:32 AM
3 1,040
Show that (p-1)(p-2)...(p-r)==(-1)^r*r!(mod p) for r=1, 2, ..., p-1. I am having trouble getting this proof started....
Feb24-10 03:38 PM
3 1,878
1) Definition: Let m denote a positive integer and a any integer such that gcd(a,m)=1. Let h be the smallest positive...
Mar1-10 09:49 PM
3 1,942
Hello there, I have trouble understanding why the coefficients in an affine combination should add up to 1; From...
Mar9-10 04:17 AM
3 2,532
given the sequence (power series) g(x)= \sum_{n\ge 0}a(n)(-1)^{n}x^{n} if i define ...
Mar14-10 01:42 PM
3 1,287
How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the...
Mar20-10 08:44 PM
3 1,056
G,H be groups(finite or infinite) Prove that if (G:H)=n, then there exist some normal subgroup K of G (G:K)≤n!...
Mar22-10 08:23 AM
3 1,188
Let f, g \in \mathbb{Z} be given as follows: f = x^8 + y^8 + z^6 and g = x^3 +y^3 + z^3. Express if possible f and g...
Apr6-10 04:51 AM
3 1,725
Can anyone explain, in detail, why/why not Z/(2x) is isomorphic to Z/2Z? I know that every element in Z can be written...
Mar30-10 09:01 AM
3 2,673
I have seen that there exists two group homomorphisms from Z to Z/2Z. However, I cannot seem to understand this. I...
Mar31-10 05:20 PM
3 1,778
How can we find the determinant of a complex matrix?
Apr1-10 07:11 AM
3 5,811
I have a pretty basic question about direct sum/product of groups. Say you were given the group (Z4 x Z2, +mod2)....
Apr5-10 12:20 AM
3 2,882
My best guess is this fits in algebra, I've been scratching my head with this for a while. I have a three...
Apr11-10 01:53 PM
3 1,705
Ok so I've been working on this problem and I'm really having some struggles grasping it. Here it is: Let W be...
Apr11-10 11:45 PM
3 1,030
Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!
Apr13-10 05:52 PM
3 1,267
I have to linear equations 3x + 2y =7 and -6x + 6y= 6 when expressed as linear combination in column vector form...
May14-10 04:33 PM
3 1,353
Hi, I'm reading Shankar's Principles of QM and I find it not very clear on how exactly should I change basis of...
Apr28-10 09:23 PM
3 1,545
One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm...
Apr21-10 12:55 AM
3 1,400 AFAIK logic is all about "T"/"F" or 0/1, and boolean...
Apr26-10 02:14 PM
3 1,001
Let S be a set on which a linear order <= (less or equal) , is defined. Show that a non-empty finite subset has a max.
Apr28-10 05:17 AM
Martin Rattigan
3 832
Let A be an n x n matrix with eigenvalue \lambda . Prove that \lambda ^2 is and eigenvalue of A^2 and that if v is an...
Apr29-10 08:53 PM
3 859
First what are Idempotents? Second, If A and B are simliar matrices, show that if A is idempotent then so is B.
May5-10 09:38 AM
3 1,017

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