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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
micromass
1 34,719
can anyone please explain to me what a spanning set is? i've been having some difficulty with this for a long time and...
Nov3-11 07:51 PM
disregardthat
3 2,775
This is the problem: Suppose A\in\mathbb{R}^{n\times k} is some matrix such that its vertical rows are linearly...
Oct6-11 09:52 AM
jostpuur
3 1,873
To determine if a matrix is invertible or not, can we determine this by seeing if the determinant of the matrix is...
Sep30-11 11:50 PM
Bacle
3 1,371
Here is a bilinear map φ of two vector spaces V₁ & V₂ into another vector space N with respect to the bases B =...
Oct10-11 12:23 PM
lavinia
3 1,711
A graph can be represented by an adjacency matrix but how is that a real mathematical matrix and not just a table? A...
Oct2-11 10:07 AM
AlephZero
3 1,843
Let S be a subring of the ring of integers ℤ. Show that if 13 ∈ S and 1000 ∈ S, then S equals ℤ. I'm thinking we...
Oct4-11 08:42 PM
Bachelier
3 1,008
Now, I can show that if n is prime then Z/Zn is a field a = a b = an-2 a*b = an-1 = 1 (mod n) --> Fermat's...
Oct14-11 11:45 AM
General_Sax
3 1,962
Hello all, I have a problem to define a set of natural numbers that meet the following equation: m2+1\equiv0 ...
Sep29-11 03:14 PM
naoufelabs
3 1,935
Why is it that a metric space (X,d) always has two clopen subsets; namely {0}, and X itself? Rudin calls it...
Oct19-11 10:19 PM
Deveno
3 1,792
Let F_n and F_n+1 be successive Fibonnaci numbers. Then |(F_n+1)/(F_n) - Phi | < 1/(2(F_n)^2) Where Phi is the...
Oct18-11 03:14 PM
Matt Benesi
3 1,802
Hi guys! I need to solve a matrix. I have 3 equations, 3 unknowns, straightforward stuff. And I know it's...
Oct18-11 07:14 PM
jasonRF
3 1,712
\frac{d}{dx}f(x)=\frac{d}{dx} how to get this derivative, what is the answer? is there textbook describe it?
Oct24-11 09:39 AM
HallsofIvy
3 1,016
There exists none. What's the easiest way to prove this? Can we state that all elements of ℤ are in ℤ but not the...
Oct6-11 02:20 PM
Deveno
3 1,226
Is it possible for two planes to meet in a point instead of in a line?
Oct20-11 10:53 PM
chiro
3 1,144
When studying complex numbers/vectors/functions and so forth you constantly encounter the idea of an inner product of...
Oct23-11 10:17 AM
Fredrik
3 1,058
So i have 3 vectors: a= b= c= How do I calculate the L in order to make these vecotrs linearly dependent? ...
Oct24-11 12:49 PM
gotmejerry
3 637
1. Problem: Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|. I was doing some...
Oct26-11 08:38 PM
micromass
3 2,374
Hi, I have just begin with Linear Algebra. I came across cosets and I dont understand what is the difference...
Oct30-11 12:31 PM
Deveno
3 1,537
Hello I am trying to solve a problem that involves "the plane y=z". How exactly should I think of this plane? It's...
Oct30-11 12:48 PM
Deveno
3 878
I came across this while doing some research. Can someone help me understand this concept. x^2+1 has a root in Zp, ...
Oct29-11 09:56 PM
Bachelier
3 1,438
Do tuples exist which aren't elements of a cartesian product of sets? Can you just write an ordered list of elements...
Nov14-11 09:18 AM
eztum
3 1,404
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
lostcauses10x
3 2,201
Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables,...
Nov10-11 09:26 AM
Stephen Tashi
3 2,919
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
seshikanth
3 1,054
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
Deveno
3 2,809
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
HallsofIvy
3 1,048
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 1,851
NOT HOMEWORK. I know how to embed Sn into An+2, just with the extra transposition, etc... But how to show it can...
Nov28-11 06:20 PM
Coca_Cola
3 1,785
Hello, This is my first post on this forum, and I'm not used to the english mathematical vocabulary, I'll try my best...
Nov27-11 12:47 PM
COURAGE_WOLF
3 1,047
Hi. I need to: prove the group (Zp*,x) has exactly one element of order 2. Here, p is prime and (Zp*,x) is the set {1,...
Nov26-11 03:26 PM
micromass
3 1,918
First let me give you some definitions for the clarification of the problem: Definition (Roman, Linear Algebra) A...
Dec1-11 10:50 PM
Deveno
3 1,688
I'm having some troubles understanding the concepts of quotient algebra. May someone explain me what exactly they...
Dec7-11 08:43 PM
Deveno
3 1,390
I was recently thinking about these diophantine equations. I'm looking for solutions (x,y) in integers with d as an...
Dec6-11 05:51 AM
Petek
3 2,185
Hello everyone, I am currently learning about bases, and I am confused about different types of bases. I understand...
Dec8-11 07:13 PM
Deveno
3 1,183
I'm working on the following: "Prove that x^2 - 1=0" has infinitely many solutions in the division ring Q of...
Dec9-11 11:21 AM
alexfloo
3 1,464
Why is the inner product of two orthogonal vectors always zero? For example, in the real vector space R^n, the...
Dec11-11 01:53 PM
Simon Bridge
3 1,244
What exactly is gauss composition? I've heard of Manjul Bhargava's work, which apparently generalized gauss...
Dec19-11 09:09 AM
Mathguy15
3 4,456
Hi, This is my first post and I must worn you that I'm not a mathematician. Im just a regular blonk looking for...
Dec19-11 06:46 PM
chiro
3 2,335
Given a basis A = {a1,a2...an} we can always translate coordinates originally expressed with this basis to another...
Dec23-11 11:32 AM
lavinia
3 1,908
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
micromass
3 1,343

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