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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 35,870
I have been asked to show that in Sn the cycle (1,2,....n) only commutes with its powers. I know that cycles commute...
Jan5-12 06:19 PM
8 3,239
Hi, Algebraists: The modN reduction map r(N) from a matrix group (any group in which the elements are matrices...
Dec30-11 12:58 AM
2 1,563
Hi, I can do Dijkstra's Algorithm alright, but I always have problems with questions which have some relevance to the...
Jan2-12 06:01 AM
4 4,156
I am wondering what are the possible homomorphisms \tau : Z\overline{+} -> Z\overline{+} From this it should be...
Dec28-11 12:21 PM
2 2,035
I need some help with understanding the basics of Lie algebra theory. I suspect my problems are due to a fundamental...
Jan4-12 04:57 AM
1 1,141
I'm curious, can anyone think of a way to prove whether or not p^x - d^y = p - d, for any odd primes p,d and natural...
Dec30-11 01:27 PM
3 2,407
Hi, I am wondering if all isomorphisms between hilbert spaces are also isometries, that is, norm preserving. In...
Dec28-11 09:38 AM
17 3,117
Affine Transformation Matrix is said to be formed by initializing it using a learned projection matrix from a...
Jan3-12 08:43 PM
Avinash Raj
2 1,442
I was thinking about some similarities in the definitions of group and field, and if it would be possible to...
Dec28-11 01:49 PM
8 1,751
According to theory the eigenvalues of a completely disconnected graph (no two nodes are connected) must be all 0. But...
Dec28-11 09:00 AM
I like Serena
8 1,636
I'm trying to prove the following, which is left unproven in something I'm reading on ruler-and-compass constructions:...
Dec28-11 06:25 PM
3 1,368
Hi, I want to solve the following equation by x: Ʃ(ai^x -b)^2 = C , where Ʃ is over all i, i = 1:N, and ^...
Jan4-12 01:12 PM
7 1,614
Can someone please add more detail or give references to help explain the lines of math in "Riemann's Zeta Function"...
Jan1-12 08:06 AM
2 3,030
I was struck with the following question: Is there a linear map that's injective, but not surjective? I know full well...
Dec29-11 12:35 PM
4 2,431
I know from linear algebra that you can take two things, and if they are equal to each other then you can simply...
Jan2-12 03:05 PM
7 1,569
Hi, I'm studying my algebra and I was trying this exercise: Solve z+iz-7z-iz-6-6i=0 I found the 2 real...
Jan2-12 09:42 AM
2 1,483
The determinant of a matrix is given by the well-known formula det(A) = sump parity(p) * producti = 1...n Ai,p(i) ...
Jan7-12 11:02 AM
2 1,269
Does this concept exist? Google yields weird results that mostly have to do with programming, and Wikipedia says...
Dec31-11 02:14 PM
0 2,211
I have no trouble calculating eigenvalues but I have a hard time understanding how to use them. I know that you can...
Jan2-12 10:02 AM
2 4,967
Hi! Given a matrix A of elements A_i\;^j, which is the right transpose: A_j\;^i or A^j\;_i ?
Jan5-12 02:51 PM
4 1,141
I like to know what is best known efficient algorithm to calculate f(x)modg(x) , in which the degrees of f(x) and...
Jan10-12 06:34 PM
Stephen Tashi
1 1,854
I've had a go at trying to come up with a procedure, for the following, but not making much progress. I've googled...
Jan6-12 06:47 PM
0 1,124
I'm just revising my maths notes on matrices and I have a couple of questions, mainly about representation of...
Jan3-12 04:31 PM
2 1,435
I've been beating my head against this problem for hours. I see numerically that two expressions are equal, but I...
Jan4-12 04:37 AM
3 1,081
Hello, I was going through the same problem. From what I can see on the net, one of the relations a linear function...
Jan4-12 04:26 PM
1 942
Say I have the equation a^2 - 10b^2 = 2. So even though this is an equation in two variables and not one, I can still...
Jan6-12 06:58 PM
5 2,735
I am using the Law of Cosines to extract and angle I need from a shaft that is turning on an air engine by piston...
Jan4-12 10:59 PM
Simon Bridge
3 1,741
if f(x)modg(x) is valid(means , if it yield a remainder) then , can there be negative powers of x in f(x)? for...
Jan5-12 10:32 PM
1 1,872
Well I don't understand this equality: A^{j}_{i}*A_{j}^{k}=\delta_{i}^{k} It is true because it is the result of...
Jan5-12 12:40 PM
10 1,338
The prime numbers are the multiplicative building blocks of the integers. Even so, their distribution escapes all...
Jan8-12 04:04 AM
14 3,111
Hello I'm trying to show that the following upper bound on the matrix 2-norm is true: ...
Jan12-12 06:31 AM
3 2,146
So I need to calculate the square root of the covariance matrix \sqrt{\Sigma_tR\Sigma_t} (the matrix square root, not...
Jan11-12 12:43 PM
Stephen Tashi
2 1,840
Are there any numbers that is not considered to be a subset of a complex number subset of a + bi Where a and b...
Jan9-12 07:55 PM
3 1,785
Recently I was assigned to implement a procedure involving "3D projections" to "2D space". Supposing that 3D data is...
Jan11-12 03:38 AM
4 2,781
Let A denote an mxn matrix and let A' denote the row echelon form of it, which has d steps. We then have according to...
Jan10-12 02:36 PM
3 1,125
Hi, I have been representing complex numbers in graphical form in school recently. My teacher was telling me about a...
Jan11-12 02:59 AM
1 1,169
I'm preparing for a qualifying exam and this problem came up on a previous qual: Let A and B be nxn matrices. Show...
Jan11-12 04:07 PM
5 2,560
how does one evaluate the direct product between a group G with components that are say 2-tuple and a group H with...
Jan11-12 09:22 AM
2 1,133
What is the operator inside the Connes' approach to RH ??, he gave a trace but never says what operator is or gives or...
Jan12-12 08:29 AM
0 1,211
My apologies if this is in the wrong section.... I wasn't quite sure where to put it. If we have the "Hessian of a...
Jan12-12 10:49 AM
0 909

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