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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 35,126
I am currently taking a number theory course. The professor who teaches the course is very well known in his research...
Oct1-13 02:58 PM
10 8,957
I'm having some set theoretic qualms about the following argument for the following statement: Let V be a vector...
Sep30-13 10:42 PM
11 3,593
Is there any finite dimensional Lie algebra that is not isomorphic to any of the subalgebras contained in GL(n) ?
Sep29-13 10:49 AM
1 845
I am curious: if f and g are (complex) orthogonal functions, are f* and g also orthogonal? (* denotes complex...
Sep29-13 10:27 AM
2 749
okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because...
Sep29-13 09:50 AM
1 1,193
hello everyone.. if we have a function y=f(x) then in-order to prove linearity we try to justify according to...
Sep28-13 04:55 PM
4 852
given an sop form of a multi variable boolean expression, how to judge if it is linear or not? is (x or y) linear? ...
Sep27-13 05:22 PM
5 1,880
If AB is invertible, then A and B are invertible for square matrices A and B. I am curious about the proof of the...
Sep27-13 02:57 PM
14 8,056
Hello, Just discovered this forum as I'm so intensely curious about this question I sought out just such a place! ...
Sep24-13 03:12 PM
2 1,386
In his interesting book "Moonshine beyond the Monster", Terry Gannon proposes the interesting thought He notes...
Sep22-13 06:37 PM
0 1,268
I am not sure that this is the correct forum for this question. I have multiple sets of 3, 3D (x, y, z) points in...
Sep22-13 01:17 PM
Stephen Tashi
4 1,344
So I have been heavily trying to understand rotations. Rotations as i understand is a planar phenomenon. You need at...
Sep20-13 09:56 PM
A David
14 2,313
Is the following statement true? I am trying to see if I can use it as a lemma for a larger proof: Let ##V## be a...
Sep20-13 05:57 AM
4 1,157
I have a question that i been trying to solve which seam simple but been having trouble. Today I thought about...
Sep19-13 11:21 PM
7 981
How is the dimension of solution space is n-r, where n is the number of unknowns and r is the rank of A.
Sep19-13 08:40 AM
5 858
Hey This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from to ...
Sep18-13 10:29 AM
1 1,003
Hey! From MathWorld on solvable group: But why is that a special case? The way I understand it: the normal...
Sep18-13 07:48 AM
2 934
F(X1,...,Xn) is an invariant polynomial defined on the Lie algebra of a Lie group. The Xi here are left invariant...
Sep17-13 07:46 AM
0 921
A is orthogonal if the A^{-1} = A^{T}. Thus, AA^{T} = I. However, is the statement A is orthogonal equivalent to...
Sep17-13 02:33 AM
1 1,089
Hello. I started Gallians Contemporary Abstract Algebra today. Is it wise to go through each of the given proofs for...
Sep17-13 01:56 AM
1 960
Eigenstates of some observable O are represented by orthonormal vectors in complex Hilbert space. Is it true that...
Sep17-13 01:22 AM
James MC
6 1,059
Say I have a linear transformation T:V##\rightarrow##W. Can I necessarily say that T(V)##\subseteq##W? I feel like...
Sep16-13 01:43 PM
6 1,158
I wanted to know if there is any way of classifying the set of all non-linear multivariable functions. I wish to...
Sep16-13 01:37 PM
1 863
Hello! Is there any nice proof that if belongs to the same vectorspace as A and B, then C is in the same...
Sep16-13 11:31 AM
1 1,012
I found that the cartan subalgebra of ##sp(4,\mathbb{R})## is the algebra with diagonal matrices in...
Sep15-13 12:12 AM
4 958
The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula...
Sep14-13 03:27 PM
1 742
Let G be a group and my book defines closure as: For all a,bε G the element a*b is a well defined element of G. Then G...
Sep14-13 02:57 PM
4 901
Consider a data matrix, X, with zero empirical mean. What is zero empirical mean? Could someone please give me...
Sep13-13 04:15 PM
1 915
if X= (3, 5, 7) & Y = (2, 4, 1) What is the 3x3 covariance matrix for X & Y?
Sep13-13 04:13 PM
7 1,052
I read that scalar matrices are the center of the ring of matrices. How would I prove this? Tips are appreciated. It...
Sep12-13 10:44 AM
1 1,323 I read from the above link that- The sample covariance of N observations...
Sep12-13 05:41 AM
6 971
Let ##T: V → V ## be a linear map on a finite-dimensional vector space ##V##. Let ##W## be a T-invariant subspace of...
Sep11-13 04:46 PM
1 782
Hello, I consider the groups of rotations R=SO(2) and the group T of translations on the 2D Cartesian plane. Let's...
Sep11-13 03:33 PM
4 947
Is this true? I am studying direct sums and was wondering if the following statement holds? It seems to be true if one...
Sep10-13 11:58 PM
3 1,182
The identity map on the direct sum of V1 and V2 would be i1 composed with p1 + i2 composed with p2. Would such an...
Sep9-13 09:04 AM
1 954
I'm curious about whether a statement I conjecture about direct sums is true. Suppose that ##V## is a...
Sep8-13 05:46 PM
4 971
Hey, how would I graph the plane x + 2y + 3z = 0. We were taught to find the x,y and z intercepts and then connect...
Sep8-13 06:45 AM
2 866
Let xij be the ith independently drawn observation (i=1,...,N) on the jth random variable (j=1,...,K). These...
Sep7-13 12:39 PM
1 827
I've been thinking about a problem I made up. The solution may be trivial or very difficult as I have not given too...
Sep6-13 10:18 PM
3 890
Could someone please explain it to me what is the difference between Variance and Covariance?
Sep6-13 03:17 PM
3 825

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