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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 33,691
Hi, I have a matrix with N rows and K\cdot M \ll N columns. Is there a generic way to choose L rows s.t. the...
Aug25-13 02:34 PM
Stephen Tashi
3 813
Suppose that V and W are finite dimensional and that U is a subspace of V. If dimU≥dimV-dimW prove that there exists a...
Aug25-13 07:33 AM
6 925
Hello! The following system of linear equations has been expressed in term of column vector in the following....
Aug23-13 09:19 AM
5 1,087
If u=(3, 3 , 3) is a vector in R3 then we can draw the vector in a three dimensional space.(3=x coordinate, 3= y...
Aug22-13 01:24 PM
3 623
Suppose that ##A## is a diagonalizable ## n \times n ## matrix. Then it is similar to a diagonal matrix ##B##. My...
Aug20-13 08:54 AM
5 1,012
Is there a term for the least k such that a^k = 1 in some ring R (if it exists, specifically in a finite ring)? Is...
Aug19-13 12:50 PM
1 705
Hello, I'm following the proof for this theorem in my textbook, and there is one part of it that I can't...
Aug19-13 10:17 AM
4 983
Hi, Lets say that I have a 4x4 matrix, and am interested in projecting out the most important information in that...
Aug18-13 12:26 PM
4 766
I am trying to prove that for any two vectors x,y in ##ℂ^{n}## the product ## \langle x,y \rangle = xAy^{*} ## is an...
Aug16-13 08:41 PM
4 811
Hi all, I would like to ask about the eigenvalues of adjacency matrices of a simple undirected unweighted graph. I...
Aug16-13 03:53 PM
0 666
Similar matrices share certain properties, such as the determinant, trace, eigenvalues, and characteristic polynomial....
Aug16-13 11:50 AM
3 970
What is the sample mean of the following matrix?
Aug14-13 01:45 PM
2 710
Hi I am trying to learn how the number systems was created, and there are two very basic thing I don't get. ...
Aug13-13 08:02 PM
7 757
\renewcommand{\vec}{\mathbf{#1}} Here is an excerpt from the text: "Theorem 12.5 The only finite symmetry groups...
Aug13-13 09:02 AM
10 1,182
I have a problem with something that should be very simple,I do not no if it is programming issue or my ignorance. If...
Aug12-13 08:13 PM
3 781
I gather the modern term for a set with a closed binary operation is "magma" and that the old term "groupoid" now...
Aug12-13 12:10 AM
Stephen Tashi
2 644
Hi all, I would like to know if there exists any method to represent multidimensional vectors on a 2D plot so...
Aug11-13 11:16 PM
8 1,124
This might seem like a stupid question but would the null space of a matrix and its, say Gaussian elimination...
Aug7-13 12:46 PM
2 681
I am following Friedberg's text and having some trouble understanding some of the theorems regarding...
Aug7-13 07:32 AM
3 727
This system originates from systems of linear Diff Eqs. I am required to use the method of undetermined coefficients....
Aug6-13 04:15 PM
7 920
Could someone please help me to read the following line(in case of inner product)?
Aug6-13 10:36 AM
3 1,063
I was wondering if anybody can see where I have gone wrong here? I was given the rule, E2(E1A1)=(E2E1)A1, I can't...
Aug5-13 02:19 PM
2 725
Its been a while since I've done this stuff, and I don't have a text handy. I know that for sets, intersection...
Aug5-13 01:20 PM
1 717
I have heard about two or above dimensional plane which we can express R2 or Rn. But I never heard about...
Aug5-13 12:51 PM
1 587
I need to convexify a 2D function F:R ^2 -> R I have an analytic expression for F, but it is exceedingly...
Aug5-13 12:10 PM
0 587
The matrix is an example of a Linear Transformation, because it takes one vector and turns it into another in a...
Aug5-13 03:17 AM
2 624
What is the difference between orthogonal transformation and linear transformation?
Aug5-13 01:01 AM
6 1,375
When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't...
Aug4-13 11:49 PM
3 558
Let M be a module over the commutative ring K with unit 1. I want to prove that M \cong M \otimes K. Define \phi:M...
Aug3-13 08:42 PM
3 1,065
Do hyperbolic rotations of euclidian space and ordinary rotations of euclidian space form a group?
Aug3-13 12:18 AM
2 509
Hi, I'm getting a bit confused about the adjoint representation. I learnt about Lie algrebras using the book by...
Aug2-13 03:24 PM
0 554
Hi everyone, I would like to ask you something about vector spaces. I have the following term: S=dim(R(...
Aug2-13 10:19 AM
0 515
An eigenvector is defined as a non-zero vector 'v' such that A.v = λ.v I don't understand the motive behind this....
Aug1-13 12:02 PM
5 1,005
Suppose ##A## is a ## n \times n## matrix. Define the set ## V = \{ B | AB = BA, B \in M_{n \times n}( \mathbb{F})...
Jul31-13 11:29 PM
5 1,044
I couldn't find the words to summarize my question perfectly in the title so I will clarify my question here. Say...
Jul31-13 06:20 PM
7 750
Hello, I'm here because I lack experience and education in the subject of systems of polynomial equations...
Jul31-13 11:34 AM
Stephen Tashi
3 714
Inspired by a question in Griffiths' E&M book (1.10), I am wondering why the components of a vector do not change when...
Jul30-13 05:03 PM
25 1,586
Suppose I have some functions ## \{ y,y_{1},y_{2},...y_{n} \} \subset C^{∞} ## and suppose I know that the Wronskian...
Jul30-13 12:42 PM
1 532
Any given representation (some matrices of some algebra) will be reducible if there exists a singular, but nonzero...
Jul30-13 03:26 AM
6 651
Take a look at this theorem. Is it a way to show this theorem? I...
Jul30-13 01:23 AM
3 603

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