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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 35,974
Hi All, In Ken Onos lecture he mentions Hausdorff dimensions appertaining to prime numbers: 5,7,11 relate to 0...
Jun8-11 06:11 PM
8 2,821
I have a matrix A, which contains only positive real elements. A is a differentiable function of t. Are the...
Jun8-11 12:24 PM
11 2,308
Here's a nice problem: Prove that \frac{k!}{k^k} \leq \frac{(k-j)!}{(k-j)^{k-j}} \frac{j!}{j^j} for all...
Jun7-11 11:02 AM
11 2,621
Hi, What is the geometric interpretation of the Gram-Schmidt orthonormalization process? I mean, you will find...
Jun9-11 12:04 PM
5 1,591
For any natural number a and b, with b > 1, two natural numbers x and y can always be found such that b^x - b^y is...
Jun13-11 01:10 AM
5 2,473
I probably can remember the matrices by just trying to, but I hate having to "remember" things without actually...
Jun6-11 02:13 PM
5 1,630
I'm having difficulty understanding the concepts presented in the following question. I'm given a matrix, , which...
Jun8-11 03:55 PM
3 2,160
Greetings. This is my first post, please be gentle! I am a music theorist who uses a lot of math in my...
Jun6-11 07:33 PM
2 1,605
Suppose I have a MxN matrix and each column may contain exactly 1 zero or no zeros. Is there a transformation that...
Jun6-11 07:34 PM
0 917
I want to see if the matrix w = (1,0;0,1) is a linear combination of the matrices v1 = (1,2;-2,1) and v2 =...
Jun6-11 09:00 PM
4 5,006
I know this question has been asked here many times before but perhaps you can give me some tailored help. I am trying...
Jun6-11 09:51 PM
cap'n ahab
0 1,292
Suppose N is a 2x2 complex matrix such that N^2=0. Prove that either N=0 or N is similar over C to the matrix 00...
Jun7-11 07:36 PM
3 1,534
Hi, Is every matrix similar to a triangular matrix? If it is, anyone have an idea how to prove it? Thanks
Jun13-11 03:37 AM
3 1,301
I've got something like u + LuL^T = v and I want to write it like u = B_1 v B_2 for some B_1 and B_2. Assume L...
Jun7-11 04:09 AM
Petr Mugver
1 1,316
I discovered a link between my series formulation, see below, and RNA molecule structure, In particular the RNA...
Jun7-11 05:49 AM
0 961
If v is in Rn and is an eigenvector of matrix A, and P is an invertible matrix, how would you go about finding an...
Jun8-11 09:28 AM
4 2,718
hey i want to find out if the set s = {t2-2t , t3+8 , t3-t2 , t2-4} spans P3 For vectors, i would setup a matrix...
Jun8-11 06:16 PM
6 3,786
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
0 455
Let p be a prime number and d / p-1 . Then which of the following statements about the congruence? x ^d = 1( mod...
Jun8-11 04:04 PM
6 1,720
hey i have the set s = {(t,1,1),(1,t,1),(1,1,t)} and i want to find for which values of t this set is linearly...
Jun9-11 06:15 PM
8 2,813
I have two systems of linear differential equations: \frac{dx}{dt}=Ax, \frac{dy}{dt}=By x,y are vectors of length n...
Jun10-11 06:00 PM
2 794
* I have already posted this in the General Math, but I guess the problem is more like a linear algebra problem. ...
Jun9-11 04:41 AM
2 1,037
Jun9-11 03:05 AM
0 1,346
Is it possible for a variable to exit the basis and after a couple of iterations, enter it again? Are there any...
Jun9-11 09:31 AM
0 496
Arg\xi (1/2+iz) however i am a bit ashamed because the Riemann Xi function is real for real 'z' so for ALL the...
Jun11-11 04:35 PM
2 1,785
How to prove that two reciprocal basis are either both right ended or both left-handed? If (e_1,e_2,e_3) and...
Jun11-11 04:21 PM
1 786
Hi, All: I have seen Orthogonal groups defined in relation to a pair (V,q) , where V is a vector space , and q...
Jun10-11 09:11 PM
0 487
With normal vectors i usually check there is the correct number of vectors i.e 3 for R3 2 for R2 etc and then just...
Jun12-11 07:11 AM
10 2,165
polynomial? i find this but i do not understand;its too complex. ...
Jun11-11 07:16 AM
2 2,403
Hi, I have this problem, 1) Find 1 + 2 + + n by summing the identity (m + 1)2 − m2 = 2m + 1 from m = 1 to...
Jun12-11 10:31 PM
2 1,882
Suppose that the set of functions \{P^a:\mathcal S\rightarrow \mathcal L|\,a\in \mathcal L\} has the property that for...
Jun11-11 07:26 PM
2 666
does multiplying the invertible matrix A to the basis {X1,X2,X3..Xn} create a new basis; {AX1,AX2,Ax3..AXn}? where Xn...
Jun13-11 02:48 AM
4 1,806
Hey everyone, Not sure if this is the right section to post this in, but makes the most sense to me so here goes. ...
Jun11-11 10:52 PM
0 1,224
Hi, I'm currently doing a project and this topic has come up. Are there any known famous classes of polynomials...
Jun12-11 01:18 PM
8 1,296
\lambda_i(AB)\leq\lambda_i(A)\lambda_i(B)? \lambda_i(A+B)\leq\lambda_i(A)+\lambda_i(B)?...
Jun13-11 02:10 AM
0 688
lets assume the matrix multiplication AB exists, how would i prove that the column space of AB is contained in the...
Jun13-11 03:01 AM
3 4,309
For two matrices A and B, when p(A)=0 iff p(B)=0 for any polynomial, what will happen? i read that A and B have the...
Jun13-11 02:13 PM
2 1,276
Hi! Q is postive definite A is any matrix. Why Q^{-1}AQ^{-1} is hermitian??
Jun13-11 04:17 AM
1 655
If S^{-1}BS=A, can we always find Q ,such that Q^{-1}BQ=A? Q different form S and no scalar multiple of S. If not,...
Jun13-11 05:54 AM
1 683
Hi folks. This is something I've been wondering about for a while now. Is there a reason why taking the minimum norm...
Jun13-11 10:23 AM
1 831

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