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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 35,094
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
1 915
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 4,700
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 2,267
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
1 739
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 1,511
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
0 983
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 7,822
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
2 496
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 2,834
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 1,972
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 1,523
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 8,794
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 1,567
I've seen in multiple sources that a linear transformation constitutes a tensor with one contravariant and one...
Dec10-11 09:31 PM
6 1,965
Does this concept exist? Google yields weird results that mostly have to do with programming, and Wikipedia says...
Dec31-11 02:14 PM
0 2,188
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 1,225
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 2,172
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 2,541
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 1,563
How can i prove that square of an integer ends with 0,1,4,5,6,9 ?
Sep1-09 06:34 AM
2 1,591
How does the exponential function work
Jun30-12 06:23 AM
2 877
This is probably very trivial, but I can't find an argument, why the orthochronal transformations (i.e. those for...
Feb19-09 07:02 AM
14 1,794
The complexified Lie algebra of the Lorentz group can be written as a direct sum of two commuting complexified Lie...
Oct14-09 10:57 PM
1 1,040
Hello, it's been a while since i did linear algebra. i need some help. I have this matrix: 1 1 0 0 1 0 0 0...
Mar25-12 08:34 PM
1 1,510
Hi everyone. Is there any way to set demands on least square solutions? I have an equation on the form Ax=b,...
Mar21-13 07:59 AM
4 1,000
Let G be a connected reductive algebraic group over an algebraically closed field of positive characteristic. Let P be...
Aug22-10 01:56 PM
0 714
I haven' been able to find good explanations of either of these: Part 1: Jordan Normal Form: Is this it? An...
Dec4-08 05:42 AM
Master J
2 1,839
A Hermitian matrix is a square matrix that is equal to it's conjugate transpose. Now lets say I have a Hermitian...
May2-11 03:59 PM
1 1,939
I'm learning about rings, fields, vector spaces and so forth. The book I have states: "Real-valued functions on...
Feb16-12 03:54 PM
10 1,988
The general linear group of a vector space GL(V) is the group who's set is the set of all linear maps from V to V that...
Feb21-12 07:54 PM
11 1,676
In studying vector spaces, I came across the coset of a vector space. We have an equivalence relation defined as ...
Mar2-12 02:10 PM
9 1,247
Wrong thread - delete this.
Aug14-07 11:55 PM
0 5,240
Theorem Let A be a square matrix nXn then exp(At) can be written as exp(At)=\alpha_{n-1}A^{n-1}t^{n-1} +...
Jan29-09 10:58 AM
3 8,410
I'm trying to understand this paper on the representation of SU(2). I know these definitions: A representation of...
Mar23-09 12:53 PM
3 1,158
I'm trying to understand this paper which the author claimed that he had constructed an infinite dimensional...
Apr6-09 01:06 AM
6 1,768
I have a system of linear equations which can be expressed as XA=Y where X and Y are row vectors. The vector Y and the...
Nov3-09 08:42 AM
5 2,264
Matlab help state that the square root of X = \begin{pmatrix} 7 & 10 \\ 15 & 22 \end{pmatrix} are A =...
Dec14-10 09:19 AM
11 5,669
Given n by n matrices A, B, C. I know how to solve the Sylvester equation AX + XB + C = 0 using the matlab...
Mar26-12 03:24 AM
3 1,568
If ##\hat{A}\vec{X}=\lambda\vec{X}## then ##\hat{A}^{-1}\vec{X}=\frac{1}{\lambda}\vec{X}## And what if...
Nov1-12 10:07 PM
4 733
Linear operator A is defined as A(C_1f(x)+C_2g(x))=C_1Af(x)+C_2Ag(x) Question. Is A=5 a linear operator? I know that...
Feb18-13 04:42 PM
6 685

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