# 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 Views: 2,205 Announcement: Follow us on social media and spread the word about PF! Jan16-12 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 35,917 If A\in\mathbb{C}^{N\times N} is some complex matrix, is there anything we could say about the determinant of the... Dec22-12 08:15 AM sfn17 2 5,320 Hi, I was playing with Riemann zeta function on mathematica. I encountered with a quite interesting result. I iterated... Dec22-12 09:48 PM Jeff Cook 10 2,082 Let B={b1,b2} and C={c1,c2} be basis. Then the change of coordinate matrix P(C to B) involves the C-coordinate vectors... Dec19-12 10:20 PM bonfire09 2 1,029 Apart from simplifying matrix powers, why do we want to diagonalize a matrix? Do they have any appealing application... Dec22-12 06:03 PM marxLynx 4 1,278 I know that we say two representations R and R' of a group G is equivalent if there exists a unitary matrix U such... Dec21-12 07:51 PM micromass 2 816 Hello everyone, first time poster, long time reader here! I'm an ex-math major and while I'm no longer pursuing a... Dec21-12 04:15 PM johnqwertyful 5 1,082 Hey all, I have been playing around with a special type of matrix and am wondering if anyone knows of some literature... Dec30-12 11:21 PM orthogonal 4 1,474 I am reading linear algebra by Georgi Shilov. It is my first encounter with linear algebra. After defining what a... Dec21-12 06:23 PM Fredrik 5 1,220 Getting ready for linear algebra exam. One question that I got right but not exactly sure why is this: ---... Dec21-12 03:38 PM Frogeyedpeas 4 1,092 I have been trying to prove the following result: If A is real symmetric matrix with an eigenvalue lambda of... Dec22-12 04:54 AM matqkks 2 1,047 What is the best way of introducing singular value decomposition (SVD) on a linear algebra course? Why is it so... Dec22-12 03:19 PM Stephen Tashi 2 762 Imagine we have two operators A and B on a complex hilbert space H such that: \psi = (AB-BA) \psi=c \psi \ \ \ \... Dec22-12 10:42 PM micromass 6 1,113 Prof. Hugh Montgomery has been quoted as saying that it appeared that, if the Riemann hypothesis is true, the... Dec23-12 10:37 AM nomadreid 0 870 Hello, I have a simple(or not?) math problem: I have equations of 3 lines in R3 trought the origin: line l1: ... Jan1-13 08:12 PM chiro 5 1,390 Hello, I was wondering, why is the vector projection useful in the way that it is presented? Why isnt just the... Dec27-12 03:30 AM Stephen Tashi 12 2,226 Question is : If m,k,n are natural numbers and n>1, prove that we cannot have m(m+1)=kn. My attempt : Using... Dec27-12 12:16 PM mathwonk 16 2,998 I have an equation (constraint) which I wish to solve explicitly in terms of gd (or more precisely a scaling factor of... Dec25-12 02:42 AM james1234 1 862 Video illustration Hello, Me and a friend, David Barrack, are non-mathematicians but we've been having fun... Dec25-12 11:34 AM micromass 2 2,050 I was looking for a hint on a problem in my professor's notes (class is over and I was just auditing). I want to... Dec28-12 06:42 AM sammycaps 12 1,306 The logic that odd composite with least difference will be factored easily and large difference would factored hardly... Jan1-13 09:30 AM mfb 4 1,647 I've got a general question about Lie algebras, which is basically this: Q: What is there to be said about the Lie... Dec27-12 01:10 AM Couchyam 0 761 This may be a very silly question, but still apologies, I read in Sheldon Axler, that the inner product of two... Dec27-12 07:31 AM vish_maths 3 858 The book I am going through says this : The below proposition is false for real inner product spaces. As an... Dec28-12 06:46 PM chiro 3 999 Is there any algorithm to form a magic square of any size with a desired magic sum ? Also can we make a magic square... Dec30-12 08:09 AM RamaWolf 6 2,128 Hi All, I have a hard time answering the following. I need some help. Let Z={a,b,c,d,e,f} and let X denote the... Dec30-12 01:31 PM laptopmarch 1 752 Theorem : if S ={ v1 , .... , vn} spans the V.Space V , L={w1 , .... , wm} is set of linear independent vectors... Jan1-13 07:55 PM mathwonk 10 1,562 Suppose that a = aBc where a and c are vectors and B is some matrix that changes as time "continuously" goes on -... Dec31-12 04:20 AM dotiozeros 0 807 Consider an m x n table containing single digits 0 to 9. So each cell contain the digits 0 to 9. My goal is to make... Jan3-13 11:01 AM mfb 7 2,253 Hello everyone, I found that you're actively discussing math problems here and thought to share my problem with... Jan1-13 03:33 AM phd_student 0 1,017 Hello everyone! I'm a 1st grade student in a slovenian high school. Recently, I've became very intrested in numbers... Jan6-13 09:22 PM skiller 11 2,352 Hi. Define a linear mapping F: M2-->M2 by F(X)=AX-XA for a matrix A, and find a basis for the nullspace and the... Jan2-13 11:59 PM nickthegreek 2 924 I'm trying to compute the complexity of the quadratic program: \displaystyle\min_{\mathbf{X}} (\mathbf{X^TQX +C^TX})... Jan3-13 08:41 PM lavinia 3 767 Why do we have x-axis perpendicular to y-axis? Why not 45° or something else? Even if we keep any other angle other... Jan5-13 12:16 PM Studiot 9 1,634 Hello all, I have a question: assume in matrix M(n*n), each element M(i,j) of matrix is computed as M(i&)*M(&j) /... Jan6-13 01:06 PM sanaz 4 1,000 I have some technical questions about spans and bases which my textbook really does not cover very well. I would... Jan6-13 06:16 PM AlephZero 2 923 I am a bit confused about the page that I attached... I don't understand part (ii)... How can you compute XX? So... Jan6-13 12:07 AM Artusartos 6 837 Hi I am going through Sheldon Axler - Linear Algebra Done right. The book States the Complex Spectral Theorem as :... Jan7-13 11:38 AM vish_maths 4 1,146 I have no idea what this is! Please can someone explain comparing to a 3x3 matrix? Jan6-13 05:19 PM mfb 3 1,106 No not the trival solution but generally GCD(x,y) = 1 when GCD(A,B)=1 x =... Jan7-13 12:40 AM ramsey2879 0 1,010 I recently got (re)interested in C* algebras. Poking around, I gathered that there is some way of constructing a C*... Jan7-13 12:17 PM marcus 0 571