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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 35,971
1. The problem statement, all variables and given/known data Let F be a subfield of K. A, B be elements of Mn(F)....
Mar13-11 11:39 PM
0 729
In linear algebra, we are now learning about digraphs and I am somewhat confused as to how we can obtain and use...
Apr18-08 03:45 PM
2 3,147
Hi there! I have to solve the following equation: 5x+6y = 40 and find out every pair (x,y) from Z that...
Nov9-08 01:01 PM
17 2,051
Hi there! Ive come upon the following problem: I want to determine the set of all lines of the following surface:...
Nov1-08 03:56 PM
3 1,535
Hi all! The prof for "theoretical methods in physics" mentioned last week the term "wedge product" but it all...
Nov13-08 11:42 PM
5 6,467
Hi! I want to determine which of the subgropus of the symmetric group S(3) are normal. The condition is: for...
Nov9-08 01:05 PM
8 1,867
Hi there! I need a little help from your side. Could you give me an example of a quadratic number in Z3 there is...
Nov16-08 05:23 AM
2 4,991
Hi all! Im trying to prove following two inequalities but I somehow got stuck: U, W are subspaces of V with...
Nov21-08 05:33 PM
3 1,457
Hi all! Does anyone know a general method for determining the image of a lin map? Im aware of the definition if...
Nov24-08 08:50 AM
5 3,738
Hi all! I want to determine to matrices, S and T, so that for the matrix B, ...
Dec7-08 02:09 PM
2 1,962
Hi all! I was wondering what conditions must two linear maps obey in order to commute? If they are described by...
Apr2-09 10:13 AM
4 1,094
Hi! I was doing an assignment in quantum mechanics and came upon the following fact I cannot explain to me. I...
Feb15-10 12:06 PM
2 1,026
Hi there! I'm trying to prove the following obvious statement, but am somehow stuck :( Let \vec a,\ \vec...
May5-10 10:42 PM
4 1,896
I have a trouble proving that a finate (nonzero) commutative ring with no zero divisors must have an identity with...
Oct27-07 04:54 PM
1 1,681
please i need your help! prove: "A nonempty set of real numbers bounded from below has a greatest lower bound."
Apr6-07 12:18 PM
6 5,405
In sieve method, we could get the prime numbers between p and p^2 applying the primes less than prime number p. Is...
May7-06 03:40 PM
5 1,633
PROBLEM: For any number in any base at least 2 digits long, if you add them together and solve it the answer will...
May6-04 07:04 PM
10 2,024
Hello everyone, I'm a bit of beginner to the more complicated algebra and geometry. Im going in to grade 12 next...
Aug30-04 08:48 PM
4 2,143
What's an example of a group that has finitely many generators, but cannot be presented using only finitely many...
Sep4-12 09:54 PM
1 933
Is there something you can do to a ring to produce a commutative ring? Like for any group, you can create an Abelian...
Nov2-10 08:09 AM
5 979
For a commutative ring R and an ideal I, is it true that I \oplus R/I \cong R ? I know in some cases this is true, and...
Jan26-11 05:52 PM
6 2,556
I came across this problem today and haven't been able to figure it out... Give an example of a vector space V...
Jun10-08 11:32 AM
5 4,732
Hi folks, I know the covariance matrix and the location of a point, both of which are expressed in Cartesian...
Feb8-12 12:46 AM
Stephen Tashi
15 2,330
Could someone please help me with the following question with a guided step by step answer: Show that T = (x, y, z)...
Sep4-12 08:53 AM
1 757
HI, I was reading an article and it says that a finite group of order p^aq^b, where p, q are primes, is solvable and...
Jan28-12 09:33 AM
2 1,559
I am having trouble understanding a section in these notes: . It is on page 3. Section 3 -- Discretization of the...
Nov25-12 07:07 PM
0 1,001
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
9 7,987
Does anybody know how to create a orthonormal basis, i.e. a matrix containing orthogonal vectors of norm 1, out of a...
Apr23-13 01:26 PM
2 508
Can anyone explain me the problem of the 36-officers and the relation to finite fields ??? References to other...
Jul26-04 10:36 PM
3 2,862
Simple question that for some reason I can't reason myself through. I'm probably gonna be mad at myself when someone...
Aug3-10 08:36 PM
7 1,992
Is it possible to define positive definiteness as whether or not the matrix transforms any vector such that the...
Nov29-10 06:33 PM
0 1,531
I'm sure there are a ton of ways to interpret what the transpose of a matrix represents. Could someone just give me a...
Jan26-11 04:01 PM
8 9,011
If we're working in R^n and we consider the elements of a basis for R^n to be the column vectors of an nxn invertible...
Nov26-11 07:40 PM
1 1,615
I've seen in multiple sources that a linear transformation constitutes a tensor with one contravariant and one...
Dec10-11 09:31 PM
6 2,040
Does this concept exist? Google yields weird results that mostly have to do with programming, and Wikipedia says...
Dec31-11 02:14 PM
0 2,215
Does anyone know exactly what kind of mathematical object a unit (like meters, coulombs, etc.) is? Or what kind of...
Feb20-12 07:44 PM
Stephen Tashi
2 1,253
hi all~ How to evaluate the performance of a set of nonorthogonal basis? Like one in Hibert space which is most...
Jul30-08 08:52 AM
2 2,186
Hello there, I have trouble understanding why the coefficients in an affine combination should add up to 1; From...
Mar9-10 04:17 AM
3 2,570
I have array of natural numbers from 1 to n. They are divided into m groups, where m*(m-1)=n. I need all m-1...
Sep21-12 05:10 PM
2 1,599
How can i prove that square of an integer ends with 0,1,4,5,6,9 ?
Sep1-09 06:34 AM
2 1,607

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