Matrices Definition and 1000 Threads

Does anyone know an algorithm for computing kronecker products of two matrices? It's probably not that hard, but I feel like my head is about to explode ATM, so if you can help me out that'd be cool. I want to implement this in fortran... I'll give you an example; Say I want compute the...

Homework Statement Homework Equations The Attempt at a Solution I tried to see if the problem has any properties with determinants that i can apply but the properties i learned didn't involve the use of adjoint matrices so I'm kind of stumped on this one. Any hints would be...

Find dimension and ker of matrices ?? Let V be an F-vector space and (phi:v->v) be an F-linear transformation of V . Define what it means for a vector v ε V to be an eigenvector of phi and what is meant by the associated eigenvalue. This is the form of the question during my calculations I...

Hello, it is known that given two column vectors u and v with N entries, the quantity uvT is a NxN matrix, and such operation is usually called outer product (or tensor product). My questions are: 1) How can we test whether or not a matrix M is expressible as an outer product of two...

How do you solve equations that have matrices? heres an example (its just off the top of my head) 3x+y=z+4 where x=1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 and y=0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 and a follow up question; does the process change if coordinates are involved in...

So when dealing with a linear transformation, after we have computed the matrix of the linear transformation, and we are asked "is this matrix diagonalizable", I begin by finding the eigenvalues and eigenvectors using the characteristic equation. Once I have found eigenvectors, if I see these...

Homework Statement So my question is related somehow to the Fierz Identities. I'm taking a course on QFT. My teacher explained in class that instead of using the traces method one could use another, more intuitive, method. He said that we could use the fact that if we garante that we have the...

Is it ok to reduce the two matrices through row operations first before multiplying them together or will the answer no longer be row equivalent? Thanks for any input!

If I reduce two matrices using row operations before multiplying them together, will I still get a row-equivalent answer to the result I would of gotten if I hadn't reduced them? Thanks for any input!

Dear all, this is perhaps a trivial question, so I apologise in advance. Any help is greatly appreciated nonetheless. ==The Equation== The equation under consideration is: A(u)=B(v) where A and B are n times n matrices, while u and v are n-dimensional vectors. ==The Question==...

Homework Statement Let A be an n x n matrix where n \geq 2. Show that A^{\alpha} = 0 (where A^{\alpha} is the cofactor matrix and 0 here denotes the zero matrix, whose entries are the number 0) if and only if rankA \leq n-2 Homework Equations The Attempt at a Solution No idea...

I'm doing practice problems for my exam, but I don't really know how to get this one. I'd like to just be able to understand it before my test if anyone can help explain it! Prove from the definition of projection (given below) that if projv=u(sub A) then A=A^2 and A=A^T. (Hint: for the...

please look at the attachement and my attempt at the solution - hope you can help. Thanks

Homework Statement If U is a 2 x 2 unitary matrix with detU=1. Show that |TrU|≤2. Write down the explicit form ofU when TrU=±2 Homework Equations Not aware of any particular equations other than the definition of the determinant and trace. The Attempt at a Solution I have...

Homework Statement DB+CA^T-2A D=3row x 3col B=2x2 C=2row X 3col A=3row X 2col The Attempt at a Solution It is my understanding that a row of a matrix is horizontal variables and a column is the vertical variables. And for multiplication of two matrices you need the colums of...

I was wondering what fraction of 3*3 square matrices are singular? I guess if the elements are real then the answer will be vanishingly small. If however, the elements are integers, is there a way to work this number out?

Homework Statement Find the matrix representations [T]\alpha and [T]β of the following linear transformation T on ℝ3 with respect to the standard basis: \alpha = {e1, e2, e3} and β={e3, e2, e1} T(x,y,z)=(2x-3y+4z, 5x-y+2z, 4x+7y) Also, find the matrix representation of...

Homework Statement Looking for some help with the proof if possible. Vector r = x y z Rotation R = cos(θ) 0 sin(θ) 0 1 0 -sin(θ) 0 cos(θ) r' = Rr It asks me to prove that r'.r' = r.r Second part of the question is about eigenvalues, it asks me to find the three...

Hello everyone, Before I ask my question, be informed that I haven't had any formal course in linear algebra, so please forgive me if the question has a well-known answer. I have two symmetric matrices, A and B. We know the eigenvalues and eigenvectors of A, and B. Now I need to...

Hello Everyone :) I have been facing a little difficulty when encountering such kind of problems . i have also written down my line of thinking and approach which i take to solve them. So, please try to give me the correct line of thinking while solving such problems: 1. If A is invertible...

Homework Statement 6. Three disease-carrying organisms decay exponentially in seawater according to the following model: P(t) = Ae-1.5t + Be-0.3t + Ce-0.05t t 0.5, 1, 2, 3 , 4, 5, 6, 7, 9 p(t) 6, 4.4, 3.2, 2.7, 2, 1.9, 1.7, 1.4, 1.1 Estimate the initial concentration of each...

Homework Statement Write the given system in the form x'=P(t)x + f(t) x'=-3y , y'=3x Homework Equations x'=P(t)x + f(t) x(t)=c_1x_1(t)+c_2x_2(t)+...+c_nx_n(t) The Attempt at a Solution I have no idea how to start this since my teacher never covered this in our notes and the book...

Hello,i have been trying to self-study matrices topics, during that I came across two complicated problems, and I wish I could provided with help to solve them : The question asks to solve each of the following system of equations, using row reduction method (Again...I assure that my teacher has...

Hello everyone , So here is this problem which i was recently thinking about Expressing any matrix as the sum of two non singular matrices So, when i think of ways to express a matrix as sum of two matrices, the thought which comes first is : (a) Any matrix can be expressed as the sum of a...

As the title says, how can I put my matrices in columns in Latex? Say I had two matrices, \[ \left( \begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i \end{array} \right) \] and \[ \left( \begin{array}{ccc}j & k & l \\ m & n & o \\ p & q & r \end{array} \right) \] then how can I get them...

Hello, How would you/or is it possible to combine two transitional probability matrices? Say for example I have 2 matrices that both measure the probability of moving from one state to another (the states are 1, 2 and 3) Here is a picture http://dl.dropbox.com/u/54057365/All/TPM1and2.JPG...

Hi everyone, I am wondering if I can input a matrix into Matlab that contains characters. I then would like to manipulate the matrix using row changing operations. Matlab, however, will not allow me to create a matrix with letters. Is there an equivalent to a matrix for character values...

First question: If A is pd, then A^-1 is pd. Outline of answer: If A is pd, then there exists a nonsingular matrix P st A=P'P Then A^-1 = (P'P)^-1 = (P^-1) * (P^-1)' = (P^-1)' * (P^-1) 3. If (P^-1)' * (P^-1), then there exists a A^-1 that is positive definite Second question: If...

I'm trying to prove eA eB = eA + B using the power series expansion eXt = \sum_{n=0}^{\infty}Xntn/n! and so eA eB = \sum_{n=0}^{\infty}An/n! \sum_{n=0}^{\infty}Bn/n! I think the binomial theorem is the way to go: (x + y)n = \displaystyle \binom{n}{k} xn - k yk = \displaystyle...

Will the set of eigenvalues of an incident matrix derive an equivalent notion of a graph spectrum as it does with an adjacency matrix? Specifically: Let sa be the set of eigenvalues of an adjacency matrix for graph G. And, Let si be the set of eigenvalues of an incident matrix for...

Homework Statement In my main function i am filling 2 matrices. Matrix A is 18x16 and MatrixB is 16x18. Then i am multiplying them in my thread function using an array of threads. However, i am getting segmentations faults when trying to run the program. #include<stdio.h> #include<pthread.h>...

Hi, since Peskin and Schroeder pretty much suppresses the indices in every equation, I am now unable to tell if a lot of these quantities are matrices or numbers. I try to look back, but I still can't seem to figure all of these out. In the Yukawa interaction, for example, the fermion propagator...

I'm trying to prove that every nxn matrix can be written as a linear combination of matrices in GL(n,F). I know all matrices in GL(n,F) are invertible and hence have linearly independent columns and rows. I was thinking perhaps there is something about the joint bases for the n-dimensional...

Homework Statement Prove: If a matrix A commutes with all matrices B \in M_{nxn}(F), then A must be scalar - i.e., A=diag.(λ,...,λ), for some λ \in F. Homework Equations If two nxn matrices A and B commute, then AB=BA. The Attempt at a Solution I understand that if A is scalar, it...

Homework Statement Prove: Every nxn matrix can be written as a linear combination of matrices in GL(n,F). Homework Equations GL(n,F) = the set of all nxn invertible matrices over the field F together with the operation of matrix multiplication. The Attempt at a Solution I know all...

one-point compactification of space of matrices with non-negative trace Hi I'm a physicist and my question is a bit text-bookey but it is also part of the proof that the universe had a beginning...so could I ask anyway...You got q which is a continuous function of a 3 by 3 matrix where if any...

Homework Statement H10 = c1 | -s1 | 0 s1 | c1 | 0 0 | 0 | 1 H21 = c2 | -s2 | 0 s2 | c2 | 0 0 | 0 | 1 Homework Equations this is what i did H10H21 = c1c2 -s1s2 | -c1s2 - s1c2 | 0 s1c2 + c1s2...

Homework Statement Determine what the tranformation does to the square with vertices (0,0), (0,1), (1,1) and (1,0). Draw the image of the square under these tranformations. Then find the change in area of the square under these transformations. a) [1 1] [1 2] b) [0 -1] [2...

Homework Statement What proportion of 2x2 symmetric matrices with entries belonging to [0, 1] have a positive determinant? Homework Equations A^{T} = A If A = [[a, b], [c, d]] Then det(A) = ad - bc. But A is symmetric, so c = b. So det(A) = ad - b^2 So, in order for A to have a...

What is the conceptual difference between and matrix and a tensor? To me they seem like the same thing...

I tried to prove that a hermitian matrix remains hermitian under a unitary similarity transformation.I just could do it to he point shown below.Any ideas? [ ( U A U ^ {\dagger}) B ] ^ {\dagger} = B ^ {\dagger} (U A U ^ {\dagger}) ^ {\dagger} = B (U A^ {\dagger} U ^ {\dagger}) thanks

Homework Statement Give the general solution of the equation Ax=b in standard form. The matrix is this: (sorry I can't do the long bracket like there should be) [ 1 1 1 -1 0 2 0 4 1 -1 1 2 0 -2 2 0 1 -1 2 4] = A [-1 10 -3 7] = b Homework Equations None...

Hey, I have two quick questions, Does mathematica automatically find the eigenvectors and values when you find the eigensystem of a non-Hermitian matrix? I've been searching the net trying to find a way to find these vectors/values but everything I find briefly touches upon...

Hi all, I am reading a paper which contains a lot of matrices. Anyway, there is this equation: \|\mathbf{H}_3\mathbf{H}_1\mathbf{e}\|^2=\mathbf{e}^{H}\mathbf{H}_1^{H}\mathbf{H}_3^{H}\mathbf{H}_3\mathbf{H}_1\mathbf{e} where superscript H means conjugate transpose, and boldface Hs are N-by-N...

A and B are two symmetric matrices that satisfy: AB = - BA Which one of these statements are always true: a. (A-B)^2 is symmetric b. AB^2 is symmetric c. AB is invertable I tried to think of an example for such matrices, but couldn't even find 1...there must be a logical way to solve it...

Hi, All: The Wikipedia page on symplectic matrices: http://en.wikipedia.org/wiki/Symplectic_vector_space , claims that symplectic matrices are invertible , i.e., skew-symmetric nxn- matrix with entries w(b_i,b_j) , satisfying the properties: i)w(b_i,b_i)=0...

I would like to have a general formula, and I am quite sure it must exist, for: \gamma^{\mu}_{ab}\gamma_{\mu \,\alpha\beta} but I didn't succeed at deriving it, or intuiting it, I am troubled by the fact that it must mix dotted and undotted indices.

Hi, I was just wondering, as I find matrices fascinating, I don't know why, but I was wondering if there was ever a use for 3D ones and if so what would be their application? It just occurred to me as I was reading about holographic hard disc storage. Curiously Rob K

Hey guys, Here is my question. A is a 4x4 matrix and there are two vectors, b and c, which have 4 real numbers. If we are told that A(vector x)=(vector b) has an unique solution, how many solutions does A(vector x)=(vector c) have? I honestly have no idea how to do this. I know that for A...

I'm preparing for a qualifying exam and this problem came up on a previous qual: Let A and B be nxn matrices. Show that if A + B = AB then AB=BA.