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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 35,963
for dimension 2, the following relation between determinant and trace of a square matrix A is true: det A=((Tr...
Nov22-11 03:22 PM
I like Serena
3 1,896
I'm having a bit of a problem understanding the kernal of a subgroup. It appears to always be equal to the identity...
Nov22-11 11:01 AM
8 1,431
Let P and Q be two points and N a vector space in 3-space. Let P' be the point of intersection of the line through P,...
Nov22-11 06:20 AM
1 1,257
Ax=0 has only trivial solution if A is row equivalent to I. Here in theorem 6 they explain it by referring to another...
Nov22-11 03:43 AM
5 5,531
let π be a product of disjoint m-cycles. Prove that π is a power of a cycle? So this is like asking show that π =...
Nov22-11 03:01 AM
4 1,259
Are all groups nonempty? If so, is it because all groups have an identity (element)?
Nov22-11 01:03 AM
1 752
When I was in grade school my father told me about a method of checking my addition when I added columns of numbers. ...
Nov21-11 04:09 PM
4 2,196
My question is really simple, but I just have to get it confirmed: for a matrix A, if det(A)=0 that means A has no...
Nov21-11 12:17 PM
6 2,262
I am working on classifying all groups of order less than or equal to 100. For most orders, this is fairly...
Nov21-11 11:14 AM
0 900
This book says that if W^aX_a=0 and X_a is arbitrary, then I should be able to prove that W^a=0. I don't see how this...
Nov21-11 06:59 AM
2 1,394
I've formulated the game Flip It( into mathematical terms and a...
Nov20-11 02:37 PM
1 1,631
An augmented matrix scaled by a number also means the solutions set is scaled by that same number. I believe this is...
Nov20-11 02:27 AM
2 1,040
because the only thing the definition asks to check is the closure and inverse axioms? this arose from a problem I...
Nov20-11 12:22 AM
4 1,154
why arent non continuous functions in an interval a linear space?
Nov19-11 08:23 AM
9 1,254
tan(x)=k\frac{x}{z^{2}} where k is the constant of proportionality, y varies according to x and z. x and z are...
Nov19-11 08:21 AM
3 1,069
If p is prime and (a, p) = 1, show that x^2 \cong a (mod p) has solutions if a^{\frac{p-1}{2}} \cong 1 (mod p) and...
Nov19-11 06:19 AM
5 2,733
Hi, not sure if this is the right forum.. pls move if not. Almost 30 years ago, I was studying engineering and my...
Nov18-11 05:54 PM
6 2,604
how can we show that proj(a+b) = proj a + proj b on an arbitrary line. My book has a proof but it assumes that the...
Nov18-11 12:24 AM
0 859
I have to prove: Consider V=F^{n}. Let \mathbf{v}\in V/\{e_{1},e_{2},...,e_{n}\}. Prove...
Nov17-11 07:54 PM
2 1,208
I am looking to find an arbitrary digit of lets say 23^234. This one has 219 digits. so lets find the 187th digit.... ...
Nov17-11 07:50 PM
2 2,269
This sieve is similar to the Sieve of Eratosthenes but is very different in its implementation. Instead of considering...
Nov17-11 07:46 PM
23 6,634
I'm trying to find a general formula for an algebraic equation, I'm studying the behavior of...
Nov17-11 07:43 PM
2 2,676
If R is a finite ring and its additive group is cyclic, then R = <r> = {nr : n an integer} for some r in R. r^2 is...
Nov17-11 05:50 PM
1 1,089
Restrict attention to vectors in ℝ^m where m is a natural number. Let σ be the vector of ones. Let V be the set of...
Nov17-11 05:35 PM
13 2,072
I think a best informal way to state the theorem is Hardy's: every positive integer (except the number 1) can be...
Nov17-11 11:47 AM
4 2,573
Can you calculate eigenvalues and eigenvectors for rotation matrices the same way you would for a regular matrix? ...
Nov16-11 08:39 PM
5 2,054
Please note: Below, I keep trying to put but it gets turned into !! In Dennery and Krzywicki, they give an...
Nov16-11 05:56 PM
4 1,433
So I just want to give a little background. I'm Chandler Baker and love all there is to life: philosophy, etc... I...
Nov16-11 05:35 PM
1 1,650
Is there a way within reasonable errors to say what part of the positive integers are prime and what part is factored...
Nov16-11 05:29 PM
3 2,252
Say I have (a+b+c)^n and I want to split it apart into a^something + b^something + c^something. Is this easily done?
Nov16-11 02:45 PM
1 1,793
As we know grad F (F surface) is in normal direction. But we also have (grad F(r)) x r = F'(r) (r) x r = 0 this...
Nov16-11 10:10 AM
3 1,080
I have to prove: Let u_{1} and u_{2} be nonzero vectors in vector space U. Show that {u_{1},u_{2}} is linearly...
Nov16-11 07:56 AM
10 2,445
Hi guys, I always wanted to know if one could generate prime numbers according to an equation,so I wanted to go and...
Nov16-11 07:18 AM
21 5,758
Having worked on prime ideals recently and finding them for Z_n I was wondering how you can to find all the prime...
Nov15-11 03:52 PM
1 1,783
Divisor summatory function is a function that is a sum over the divisor function. It can be visualized as the count of...
Nov15-11 09:05 AM
18 7,529
Hi everyone. My first post on this great forum, keep up all the good ideas. Apologies if this is in the wrong...
Nov15-11 05:18 AM
1 1,783
I have read at a lot of places that in 2D transformations rotation is a combination of scaling and simultaneous shear?...
Nov15-11 04:18 AM
3 2,885
Which of the transformations are onto? 1) T:R2 -> R2, where T(x,y) = (5x-y, 0) I don't know if I'm understanding...
Nov15-11 03:47 AM
1 1,514
Let Fn = 22n + 1 be the nth Fermat number and suppose that p|Fn, where p is a prime (possibly Fn itself). Show that ...
Nov14-11 10:25 PM
4 2,100
If we take the derivative of n functions that are linearly independent to each other and we write it down like c1f1(x)...
Nov14-11 03:30 PM
8 2,260

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