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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 35,921
Hi this is my first post on this site and glad to be here! Ive only really started looking into maths and physics...
Sep21-12 10:05 PM
5 2,085
Hello I'm reading my old notes of QM, I found the definition of Pauli vector, as follow \vec{\sigma}=\sigma_1...
Sep18-12 10:42 AM
4 2,105
Hello Forum, a system of linear equations can be determined (if there are as many unknowns as equations),...
Sep17-12 10:56 AM
15 2,643
Consider the separation of the Riemann Zeta function in two terms \begin{flalign*} \zeta(s) &= 1^{-s} + 2^{-s} +...
Sep19-12 04:01 PM
3 2,173
I know that one of Goldbach's conjectures is that every even number is the sum of 2 primes. So, I was wondering if...
Sep22-12 01:48 PM
6 4,237
How important are linear transformations in linear algebra? In some texts linear transformations are introduced first...
Sep28-12 06:40 PM
4 1,300
Hi all. I'm studying from Leon's Linear Algebra with Applications. I'm wondering if one of his examples has an error....
Sep18-12 11:37 PM
4 1,391
I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the...
Sep19-12 12:24 AM
2 1,029
Hi, I have a problem from a textbook on control systems along with the solution, but I'm not certain how the answer...
Sep24-12 10:52 AM
The Electrician
7 1,403
I am trying to prove that 11 is a prime in \mathbb{Z}. I noticed that \mathbb{Z} is not a UFD so I cannot show that...
Sep17-12 11:42 AM
2 1,097
I'm trying to find if a number is odd or not, basically if X % 2 = 1. Can this be expressed through some function?...
Sep25-12 08:48 AM
13 2,165
Hi. I'm wondering if anyone can point me to any information on techniques to decompose a matrix (actually a 3D...
Sep17-12 03:04 PM
Stephen Tashi
6 1,875
Let $${x_1,x_2,...x_n}$$ be positive numbers. Consider the matrix C whose (i,j)-th entry is ...
Sep17-12 10:21 AM
0 801
Why are QR factorization useful and important?
Sep18-12 11:05 AM
1 719
Hello, Scilab help states that If a matrix is badly scaled or nearly singular, a warning message will be...
Sep23-12 11:46 AM
14 4,727
Say I have a mxn matrix A and a nxk matrix B. How do you prove that the matrix C = AB is full-rank, as well?
Sep22-12 03:13 PM
6 2,145
In 'Linear Algebra Done Right' by Sheldon Axler, a direct sum is defined the following way, We say that V is the...
Sep19-12 02:02 PM
2 741
Am I right in saying that Zp x Zp (the product of the integers mod p, a prime, with itself) has only 3 nontrivial...
Sep19-12 09:41 PM
2 1,237
How can I prove that the set of all planar vector fields forms a vector space? Thanks for any input!
Sep20-12 12:50 AM
2 1,456
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 1,590
I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which...
Sep22-12 10:24 PM
6 1,754
Suppose there is a set of complex variables \{x_i,\,i=1 \ldots M;\;\;y_k,\,k=1 \ldots N\} and a polynomial...
Sep24-12 04:08 AM
5 1,081
Does anyone know of a general approach towards the problem posted here: It...
Sep21-12 05:02 PM
0 623
I'm reviewing Projective Geometry. This is an exercise in 2D homogeneous points and lines. It is not a homework...
Sep22-12 05:40 PM
5 1,218
Hello forum, why does a system of linear equations really have no solution or one unique solution, or infinite...
Sep23-12 02:42 PM
7 1,145
I have to prove "For every integer n, n^2 is congruent to exactly one 0,2,or 4mod 7? I don't even know where to start?...
Sep26-12 05:17 PM
17 2,782
Find two algebraic numbers (over Q) a and b each of degree 3 such that ab has degree 2. I have attempted to...
Sep24-12 10:04 AM
0 578
Okay, so for the problem before this, I proved that L(S ∩ T ) ⊂ L(S ) ∩ L(T ). For this problem, I have to give...
Sep23-12 09:42 PM
1 623
Hi Can someone please clarify if you are trying to diagonalize a matrix and you find that one of your eigenvalue is...
Sep24-12 04:58 PM
4 958
Hi, A quick question: Does a set need to be a subset to be a subspace of some vector space?
Sep24-12 09:22 AM
3 771
Prove that the polynomial $$x^{20}-2x^{13}+10x^{7}-6x^{2}-4x+100\in\mathbb{Z}$$ is irreducible or factors into...
Sep24-12 09:57 AM
0 577
Find the general solution to the following system of equations and indicate which variables are free and which are...
Sep24-12 09:03 PM
Simon Bridge
1 842
u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku =...
Sep26-12 10:29 AM
Stephen Tashi
2 1,152
I'm required to diagonalize a 5x5 matrix by hand, using 'appropriate similarity transformations.' I'm not asking for...
Sep26-12 05:02 PM
12 1,914
Hello, I am reading a set of lecture notes on lattice QCD:...
Sep26-12 09:58 AM
0 596
I have had absolutely no sleep for a while, so my math brain has been failing me. Last night, I was working on a...
Sep28-12 10:03 AM
9 2,370
we know the equation above does not have integer solutions ( Fermat last theorem having been proven few years back )....
Sep27-12 07:24 AM
1 1,463
I am really confused about something. I know that if I have a vector space, then the dimension of that vector space...
Sep27-12 10:09 PM
5 883
When studying linear algebra when encountering a system Ax=b, I always read of the fundamental subspaces of A: N (the...
Sep28-12 07:00 PM
2 903
The assignment is making use of the property of triangular matrices to find the inverse of a matrix \displaystyle A. ...
Sep28-12 07:07 AM
0 718

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