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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 34,867
Hi! I have a question concerning solving a system of linear equations. I know that the pseudoinverse matrix by...
Sep2-13 09:50 PM
2 935
Question regarding Kronecker Delta and index notation I am reading a book which covers the Kronecker delta and...
Sep2-13 08:51 PM
16 1,844
Hi, The following equations are from linear regression model notes but there is an aspect of the matrix algebra I...
Aug30-13 09:47 PM
1 710
Trying to make sense of the following relation: \sum log d_{j} = tr log(D) with D being a diagonalized matrix. ...
Aug30-13 05:57 PM
3 752
The context in which this question arises (for me), is I was trying to take the curl of the magnetic field of a moving...
Aug30-13 05:43 AM
3 823
For example, if were given only a vector <5, 3, 1>, is this assumed to be respect with the standard basis of R^3? ...
Aug29-13 08:09 PM
Simon Bridge
10 1,027
Given A(m,n), eps = Machine Epsilon, fNorm = FrobeniusNorm(A), p >= 1 To filter noise near zero created by floating...
Aug29-13 11:44 AM
1 675
We know that the Newton binomial formula is valid for numbers in elementary algebra. Is there an equivalent formula...
Aug28-13 05:31 PM
4 806
Hello folks, I'm not even sure if this is the place to put this but with some luck it might be. I just have a...
Aug25-13 07:28 PM
5 905
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
3 838
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 1,007
Hello! The following system of linear equations has been expressed in term of column vector in the following....
Aug23-13 09:19 AM
5 1,228
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
3 636
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 1,033
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
1 719
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 1,004
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
4 788
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
4 833
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
0 681
Similar matrices share certain properties, such as the determinant, trace, eigenvalues, and characteristic polynomial....
Aug16-13 11:50 AM
3 1,086
What is the sample mean of the following matrix?
Aug14-13 01:45 PM
2 724
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
7 770
\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 1,238
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
3 800
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
2 662
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 1,148
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
2 697
I am following Friedberg's text and having some trouble understanding some of the theorems regarding...
Aug7-13 07:32 AM
3 743
This system originates from systems of linear Diff Eqs. I am required to use the method of undetermined coefficients....
Aug6-13 04:15 PM
7 939
Could someone please help me to read the following line(in case of inner product)?
Aug6-13 10:36 AM
3 1,106
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
2 750
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
1 735
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
1 596
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
0 593
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
2 635
What is the difference between orthogonal transformation and linear transformation?
Aug5-13 01:01 AM
6 1,888
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
3 571
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 1,075
Do hyperbolic rotations of euclidian space and ordinary rotations of euclidian space form a group?
Aug3-13 12:18 AM
2 520
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
0 564

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