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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 33,867
How important are linear transformations in linear algebra? In some texts linear transformations are introduced first...
Sep28-12 06:40 PM
4 1,254
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 1,355
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 2,113
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 2,700
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
4 902
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
1 830
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 1,059
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 1,830
Hello, I am reading a set of lecture notes on lattice QCD:...
Sep26-12 09:58 AM
0 550
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 2,288
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 1,424
x / y = z, so z * y = x 1 / 0 = x, so x * 0 = 1 But 0 does not equal 1, so x / 0 is unsolvable. Oh, and I'm new to...
Sep29-12 08:22 AM
6 2,298
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
5 857
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
2 884
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
0 697
I do not have access to the math calculators. Δ = 162*(a-b)*(a^2-b^2)*(a^3-b^3) -108*(a^3-b^3)*(a-b)^3 +...
Sep28-12 10:12 PM
3 1,490
if M is dxd positive semi-definite matrix, then: M = L'(or L transpose) * L where L is a matrix of dimensions...
Sep28-12 11:51 PM
0 581
Hello, Let's have a group G and two subgroups A<G and B<G such that the intersection of A and B is trivial. I...
Sep29-12 01:34 PM
2 976
Every resource I've looked at just lists the axioms but doesn't tell how or why they were arrived at. To what extent...
Sep30-12 07:10 PM
5 1,240
Say I have two matrices of the form A = (1 x 6 row vector) and B = (1 x 3 row vector). The number of...
Sep30-12 08:09 AM
2 937
As the title suggests I am working on some general relativity and combinatorics seems to be my ever-returning Achilles...
Sep30-12 04:57 AM
0 1,632
What is the field Z_{2}?
Sep30-12 09:42 AM
2 1,342
Hello, I have a subgroup S=\left\langle A \right\rangle generated by the set A, i.e. S=\left\{ a_1 a_2 \ldots a_n...
Oct1-12 07:33 PM
2 659
I'm looking for a determinant formula for a 10 by 10 matrices in variable format.
Sep30-12 10:30 PM
The Electrician
10 1,136
Dear all, I have been banging my head on this for a couple of hours with no result yet and given it is a very elegant...
Sep30-12 03:43 PM
0 581
Hello, Does anybody know about the origin for the "s" variable notation in the Laplace transform? In France, we...
Oct1-12 08:23 AM
0 649
I was doing a brain treaser where the letters A-H had to be put into an array 2 by 4 such that no letter is adjacent...
Oct4-12 07:08 AM
3 1,814
The problem: "xy + yz + zx = 12 xyz = 2 + x + y + z Find a solution of the above simultaneous equations, in...
Oct1-12 07:08 PM
2 1,348
I am having more than a little fun with this sequence of numbers and am looking for a better algorithm to find the...
Oct3-12 08:24 PM
4 1,456
If I have some path in complex plane, and I go from ##z## to ##z'## with single steps ##\alpha=1,i,-1,-i##. If I...
Oct1-12 02:19 PM
0 526
In ℝ^{3}, how would I go about proving that two planes are parallel, given their equations? I know what the "word"...
Oct2-12 04:59 AM
7 2,346
Oct1-12 09:45 PM
Greg Bernhardt
3 2,987
Hello, My problem is as follows: I want to generate a series of 24 dimensional random numbers to act as the starting...
Oct3-12 02:07 AM
Stephen Tashi
1 746
If ##g_l## is number of graphs with ##l## lines where all vertices are even, what is exactly ##D_l##? Definition...
Oct3-12 02:22 AM
0 633
1. Why is the norm of a vector noted by double pipes when it is just the magnitude which is notated by single...
Oct3-12 05:39 PM
6 1,258
Why are we interested in looking at the kernel and range (image) of a linear transformation on a linear algebra course?
Oct4-12 11:30 PM
2 876
Is the following statement true? My intuition tells me it is true, but I have been trying to prove it, without much...
Oct4-12 12:16 AM
1 787
Another vector identity I have been trying to prove. My textbook lists this identity in "properties of cross products"...
Oct4-12 12:10 AM
1 779
Suppose a matrix X of size n x p is given, n>p, with p linearly independent columns. Can it be guaranteed that there...
Oct5-12 05:13 AM
4 1,009
Using the definition given below, I wonder whether we can deduce that for each object A in C', the identity for A in...
Oct5-12 02:44 AM
1 702

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