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Linear & Abstract Algebra

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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 30,427
I'm looking at the exercises of Hungerfod's Algebra. Some looks easy but it seems the proofs are not so obvious....
Nov11-09 12:27 AM
Spartan Math
4 7,038
write all possible equivalent conditions to "A is invertible," where A is an nxn matrix.
Nov7-07 07:55 PM
morphism
7 7,026
Quick question: is the nullspace the orthogonal complement of the column space or the the row space? Thanks, sorry...
Nov22-04 05:21 AM
Galileo
2 7,011
Hi everybody, I'm new to absract algebra and I really can not understand different between direct sum and direct...
Mar14-10 11:58 AM
Landau
9 7,010
If you have two groups, G_1 and G_2 and A is a common subgroup, then you can form the free product of G_1 and G_2...
Oct25-06 10:30 PM
mathwonk
20 7,009
Cantor's diagonal slash has been used to argue that the infinity of reals is uncountable, whereas the infinity of...
Mar7-05 05:23 AM
Hurkyl
44 6,980
I'm working on some basic number theory. I came across an idea and I'm having trouble finding a general solution. A...
Jun28-07 11:08 AM
ramsey2879
3 6,975
0^0 = 1? ( 1 2 3 ... Last)
I've been told that any number raised to the zeroeth power is equal to 1. What about zero raised to the zeroeth...
May29-05 09:06 AM
matt grime
83 6,964
Hi everyone, I'm in Grade 11 this year (in Australia), currently studying from Apostol's first volume "Calculus". I...
Jan19-09 09:22 PM
wsalem
18 6,937
Just a conjecture... If any realizable real is built from the integers, then the single smallest positive real is:...
Jun21-04 01:22 AM
Jack Martinelli
16 6,929
I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one,...
Apr30-10 04:11 AM
astroultraman
20 6,919
I have to prove that if ab is divisible by the prime p, and a is not divisible by p, then b is divisible by p. In...
Aug6-04 08:10 AM
HallsofIvy
9 6,913
hmm.........
Sep30-11 05:47 PM
lostcauses10x
19 6,902
My lack of any shred of idea about the concept of the determinant is really beginning to bug me. Especially now that I...
Sep20-10 12:09 PM
mathwonk
23 6,898
A*A^T Will result in a symmetric matrix. Does this mean that A*A^T will be positive semi-definite? Does A have...
Nov20-08 12:16 AM
D H
1 6,873
Hi all, i would like to tell me, how to find the modular multiplicative inverse (MMI), of a mod n... Untill...
Dec3-10 04:38 AM
scouter
7 6,851
Prove that if A is an invertible matrix and AB = BC then B = C. I thought the way to approach it was to use A^-1 on...
Oct15-09 06:56 AM
HallsofIvy
1 6,848
I am not sure I fully understand the extension of the Unique Factorization Theorem (UFT) to Gaussian Integers (GI), by...
Jul30-08 02:54 PM
CRGreathouse
5 6,829
Given a commutative ring R with a unit, how do you prove that the product of two ideals, I1 and I2, is also an ideal?...
Aug18-08 10:28 AM
udita
9 6,814
What do you guys think of this? I haven't been able to find any sort of verification from reputable sites. "Edgar...
Oct6-06 12:08 PM
arildno
20 6,812
The question: If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive...
Sep12-08 01:50 AM
morphism
1 6,805
If G is an abelian group, a in G has order m, b in G has order n, and gcd(m,n)=1, show that ab has order mn. I am...
Jan30-04 08:44 PM
Jupiter
5 6,796
For any 10 digit natural number N in which the first digit corresponds to the total no of 1's. the 2nd digit...
Jun29-09 02:12 AM
CompuChip
9 6,793
Some physics major told me: "Linear Algebra is much more important then calculus" Can anyone give weight to these...
Apr25-09 04:05 AM
HallsofIvy
5 6,790
\ Let T: V \rightarrow W be a linear transformation, let b \in W be a fixed vector, and let x_0 \in V be a fixed...
Jun1-05 09:59 PM
mathwonk
4 6,773
What three digit prime number has all prime digits and forms primes with its first two and last two digits?
Dec17-08 11:18 PM
robert Ihnot
14 6,772
I'm trying to find the basis for a particular matrix and I get a 3 eigenvalues with two of them being identical to...
Nov9-04 11:11 AM
matt grime
1 6,753
There are two references frames, A and B. Let A's reference frame be denoted by the columns of the identity matrix,...
Dec8-10 08:33 PM
p1ayaone1
5 6,741
I read on http://www.cut-the-knot.org/blue/Euler.shtml that the derivation of the Euler's formula for \varphi(m)...
Jan17-08 05:16 AM
Eus
4 6,740
How would I calculate the determinant of a square matrix using LU Decomposition. Please be plain, I am not good with...
Aug20-09 10:11 PM
jeff1evesque
1 6,740
Does anybody know of any jobs that deal explicitly with Matrices and/or Linear Algebra? I have to do a paper and I...
Oct19-07 12:43 PM
chapani
2 6,732
Greetings, I just stumbled upon this site and thought someone might be able to help me. How many elements of order 5...
Oct6-04 11:22 AM
Motifs
2 6,731
I am trying to prove that for an integer n, if even, then n(n^2 + 20) is divisible by 48. I have done all the...
May31-05 01:49 AM
TenaliRaman
33 6,728
Hi all, I have a problem with the question below: Suppose that 2x_1 + x_2 + 3x_3 = 1 4x_1 + 6x_2 + 8x_3 = 5...
Mar30-06 08:43 PM
wu_weidong
0 6,725
I am curious as to why a subset of a vector space V must have the vector space V's zero vector be the subsets' zero...
Feb8-08 03:25 AM
mrandersdk
5 6,722
A little while ago I noticed a pattern in the sums of the digits of perfect squares that seems to suggest that: For...
Apr12-04 08:55 PM
honestrosewater
25 6,706
So I've shown that A and A^T have the same char. polynomials => same eigenvalues, using the fact that detA = detA^T. ...
Feb15-08 04:19 PM
ObsessiveMathsFreak
2 6,702
i was not sure where to put this topic since I don't know which subject of math grassmann math constitutes. Is there...
Aug21-07 07:50 PM
Chris Hillman
1 6,698
Hi all, I am trying to generalize a geometric concept found on page 7 from Steven Weinberg's "Gravitation and...
Nov18-10 11:49 PM
chingkui
4 6,695
Claim: n! + 1 and (n+1)! + 1 are relatively prime. How can we prove this? Can we use mathematical induction? Base...
Jan14-10 01:09 AM
Ivan,Cow'sSon
45 6,688

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