# Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:24 AM micromass 1 30,545 I know the definition of the Abelianization and the most direct implications of this new group, but what I don't... Mar25-10 11:53 AM Newtime 2 1,693 Hi I have the following tensor and i need to reduce to a scalor quantity: 3 by 3 matrix 4150470.48 , 317.64,... Mar25-10 07:49 AM frasool 2 1,085 Prove that the function B: L(V) -> Mnxn(R) given by T -> B is an isomorphism. B is the B-matrix for T, where T is in... Mar24-10 05:23 PM sweetiepi 2 796 Suppose I have a system of m equations in k unknowns \begin{align*} a_{11}x_1 + a_{12}x_2 + \cdots + a_{1k}x_k... Mar23-10 08:28 PM e(ho0n3 4 1,143 How do you know if the solution set of a matrix is a point, line, plane or cube? How do you know the dimension of the... Mar23-10 05:24 PM math_maj0r 2 3,195 Hello, I have a pretty decent idea about how SVD works but when I look at some of the implementation details (for... Mar23-10 04:35 PM pamparana 0 604 I hope someone can help me with this: Let the the inverse A A^{-1}=A^{-1} A=I, where I is the identity operator.... Mar23-10 12:51 PM Fredrik 1 751 Hi, first off - Go easy on me, I'm only learning :redface: My book is talking about linear independence. As I... Mar23-10 11:47 AM dacruick 9 1,217 Let R be a commutative ring with unity. I and J are ideals of R. Show that If I + J = R, then I∩J=IJ. I know that... Mar23-10 10:25 AM emptyboat 1 1,264 Hi.... I was trying to project out the two dimensional rep of S3 from its regular representation by using the... Mar23-10 04:47 AM krishna mohan 0 1,060 Q1: Let A = 1 3 0 0 -4 4 3 4 5 a) Find Cartesian equations for Col(A) and Null(A). b) Are the columns of A... Mar23-10 03:43 AM Eynstone 1 1,052 Can a non square matrix span? Mar23-10 03:39 AM Eynstone 1 557 So I'm learning about Ring Theory and have gotten to Ideals. My book tells me that the product of two ideals I and J... Mar22-10 11:03 PM Hurkyl 4 2,511 Hi I'm a high school student. I gave a proof for the following theorem, but I was told by some professors that this... Mar22-10 02:34 PM mumatics 2 1,483 Hello All I have recently recovered from a 4 year hospitalization which pretty much ended my career as a computer... Mar22-10 08:28 AM Gabriel... 6 2,416 G,H be groups(finite or infinite) Prove that if (G:H)=n, then there exist some normal subgroup K of G (G:K)≤n!... Mar22-10 08:23 AM emptyboat 3 1,150 Need to find all the posible solutions (a,b,c) for 1/a + 1/b + 1/c = 1, a,b,c integers. Mar22-10 04:56 AM im_hoogiez 14 17,071 Hi there, just a pretty straight forward query I need cleared up..... If a question asks for the null space of A... Mar22-10 02:07 AM canyonist 2 707 Hi guys, I'm trying to show that \mathbb{F}_5/(x^2+2) and \mathbb{F}_5/(x^2+3) are isomorphic as rings. As I... Mar21-10 08:54 AM JackTheLad 4 1,131 How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the... Mar20-10 08:44 PM quasar987 3 1,012 hey guys, im a student engineer and have found that the laws we use are primarily based off of stats. this has led me... Mar20-10 01:37 AM robert2734 10 1,849 Hello, Let's consider the L^2(\mathbb{R}) space with an inner product, and the complex sinusoids in the interval... Mar19-10 04:09 PM jostpuur 5 2,363 I'm an undergraduate computer-science student doing research in the field of computer vision, and one of the tasks... Mar19-10 07:06 AM mikeph 1 3,705 Hello people. I'm a freshman in college and I'm looking forward to enter an advanced mathematics program. The... Mar18-10 01:26 PM Hobold 9 7,874 If I want to know how many solutions a consistent linear system with more equations than unknowns has, how do I tell?... Mar18-10 06:49 AM HallsofIvy 1 3,230 hi, i was reading about finitely generated ideals and there was a remark that ideal which consists of... Mar18-10 05:12 AM mrbohn1 1 1,524 hi, i want to show that If R is a PID then a submodule of a cyclic R-module is also cyclic. do i need to use... Mar17-10 08:33 PM mesarmath 2 2,045 I am having the hardest time proving that "The product of any two even integers is a multiple of 4." My proof... Mar17-10 04:02 PM tiny-tim 1 1,213 Proving Axiom 1 of all 3 x 3 magic squares. I used summation notation to do so but it is extremely long and... Mar17-10 09:31 AM Zorba 4 1,335 How to prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A.... Mar17-10 09:10 AM Zorba 2 1,065 If A\in O(3) and v,w\in\mathbb{R}^3, then (Av)\times (Aw) = (\textrm{det}\;A) A(v\times w) is right, right?... Mar16-10 03:08 PM Jmf 7 3,196 Take two rows of respective length m and n: a1, a2, a3,..., am and b1, b2, b3, ..., bn. Then produce as follows... Mar16-10 02:11 PM mahch 6 1,366 Hey guys! I am having a major brain problem today, with this problem. L is a linear transform that maps... Mar16-10 11:03 AM Takuya 4 3,088 Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an... Mar16-10 10:53 AM TIMRENNER 0 1,019 Hey I'd appreciate it if somebody could "yay or nay" my understanding of the following concepts, I think I'm mixing... Mar15-10 06:46 PM sponsoredwalk 4 950 See the attachment/// Can Anyone Understand this??? I mean what metod has he followed to solve this equation for x... Mar14-10 07:28 PM phymatter 2 838 given the sequence (power series) g(x)= \sum_{n\ge 0}a(n)(-1)^{n}x^{n} if i define ... Mar14-10 01:42 PM g_edgar 3 1,247 Hi everybody, I'm new to absract algebra and I really can not understand different between direct sum and direct... Mar14-10 11:58 AM Landau 9 7,026 So an example was the matrix: A = \left(\begin{array}{cccc} a&a+b\\ b&0\\ \end{array} \right) is a... Mar14-10 11:52 AM Landau 2 2,284 Definition: A primitive Pythagorean triple is a triple of natural numbers x,y,z s.t. x^2 + y^2 = z^2 and gcd(x,y,z)=1.... Mar14-10 07:13 AM Gokul43201 8 3,686