Matrices Definition and 1000 Threads

Homework Statement Suppose that N is a nilpotent mxm matrix, N^{m}=0, but N^{m'}\neq0 for m'<m. Show that there exists a basis in which it takes the form of a single Jordan block with vanishing diagonal elements. Prove that your basis set is linearly independent. Homework Equations...

Hello, I am looking at some code which creates a projection matrix and I can verify that it is indeed correct as P^2 = P. The way they do is as follows: There is a 4x4 matrix which is an affine map between two coordinate systems (takes one from image space to world space). It is a...

Homework Statement P=\begin{pmatrix}3 & -1\\ 2 & 4 \end{pmatrix} Q=\begin{pmatrix}4 & -1\\ -2 & 1 \end{pmatrix} R=\begin{pmatrix}3 & -3\\ 2 & 4 \end{pmatrix} S=\begin{pmatrix}4 & 7\\ 9 & 1 \end{pmatrix} PX = Q QY = R RZ = S Find Matrices X, Y, and Z. Homework...

Hi, Is anyone here working with (sparse) matrices of size million by million? If so, I would like to know what software you use and any special techniques employed. PS: I am currently working a project where I need to find eigen value of huge matrices. The best I have been able to do so far...

Homework Statement Give examples to describe all 2 × 2 reduced row echelon matrices The Attempt at a Solution Not sure how to type matrices on here. I came up with 5 different ones: 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 Are there any I'm missing? i...

I have two known square matrices A and B of different order. Is there any way of constructing a transformation - e.g. a transformation matrix C - that transforms A to B? And, in that case, how do I determine C? Would it be something like this? AC = B Or maybe more general, how to determine...

Hi there, I was recently working with Kronecker product of matrices, and a question came up that I'm not sure how to answer. Is the matrix that represents a Kronecker product of two infinite dimensional matrices well defined? If yes, are some of the properties of the Kronecker product listed in...

Greetings, I have a matrix of order 5 x 5 I would like to replace the 2 elements in column 1 with 0's 1 elements in column 2 with 0's 4 elements in column 3 with 0's 3 elements in column 4 with 0's 2 elements in column 5 with 0's What are the different number of matrices...

I am wondering how one would find a the determinant of a 4x4 or greater. This isn't an urgent question, just a curiosity.

Hi there, As you know, we can represent a Linear vector operator as a matrix product, i.e., if T(u) = v, there is a matrix A that u = A.v. What about a linear operator of matrices. I have a T(X) = b where X belongs to R^n_1Xn_2 and b belongs to R^p. What is a suitable representation of...

Homework Statement I can find my eigenvalues just fine, and they're both real, as expected. My first eigenvalue is -3, which I know is correct. I have the equations 5x+(3-i)y=0, (3+i)x+2y=0 Both of the equations come from my hermitian matrix, after I substituted λ=-3. Homework...

If I had an infinite matrix \aleph_0 \times \aleph_0 could I find the eigenvalues or the Determinant of this matrix. I think some of these matrices would have a finite Determinant or it could be zero. Because i could add 1/2+1/4+1/8... but I would just need a matrix with the right entries...

Hi, I have five 6x6 matrices defined on mathematica with some unknowns and I need the final matrix let's say, mf. When I tried to find out mf with Dot[] command, it works but the result won't be so logic. On the other hand, when I tried to do this multiplication with . symbol, there exists a...

I just started learning about morphisms and I came across a problem that totally stumps me. Here goes: Show that the algebra of quaternions is isomorphic to the algebra of matrices of the form: \begin{pmatrix} \alpha & \beta \\ -\bar{\beta} & \bar{\alpha} \end{pmatrix} where α,β\inℂ...

Homework Statement Let W1 be the set of all nxn skew-symmetric matrices with entries from a field F. Assume F is not characteristic 2 and let W2 be a subspace of Mnxn(F) consisting of all nxn symmetric matrices. Prove the direct sum of W1 and W2 is Mnxn(F). Homework Equations The...

Hello Both of the below theorems are listed as properties 6 and 7 on the wikipedia page for the rank of a matrix. I want to prove the following, If A is an M by n matrix and B is a square matrix of rank n, then rank(AB) = rank(A). Apparently this is a corollary to the theorem If A...

Hi, I'm fairly new to MATLAB and I was wondering if you guys could help me out. If I have an N*N matrix, C where the (k,l)-entry is defined as: http://a3.sphotos.ak.fbcdn.net/hphotos-ak-ash3/556394_10151031836051952_2120388553_n.jpg Where x_i is from an N-vector where x_i is normally...

Does anyone have any good introduction to theories of the quark and lepton mass matrices? Theories like textures and horizontal symmetry. My understanding of research into textures is that it often involves trying to make zero as many entries as possible in the mass matrices. Is that a fair...

Homework Statement https://dl.dropbox.com/u/4788304/Screen%20shot%202012-07-08%20at%2002.53.44.JPG This is the solution of Problem A.15 in Griffiths' Quantum Mechanics. Tx is the rotation matrix about x-axis for theta degrees; while Ty is the rotation matrix about y-axis for theta degrees...

Homework Statement Find all 2x2 matrices such that A=A^-^1 (the inverse, just in case the notation is different) Homework Equations A= \begin{bmatrix} a & b \\ c & d \end{bmatrix} The Attempt at a Solution This is my second attempt at this question. The first time, I took a different...

I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!

In MATLAB, Why is sparse(rand(4)) not same as sprand(4)? Is it not supposed to be? What is the reason? Please see the interaction in MATLAB pasted below. sprand(4) ans = (1,1) 0.8147 >> rand(4) ans = 0.9058 0.0975 0.9649 0.4854 0.1270 0.2785...

Please don't mind my math english, I'm really not used to it yet.. Given R\in M_n(F) and two matrices A\in M_{n1}(F) and D\in M_{n2}(F) where n1+n2=n R = \begin{pmatrix} A & B \\ 0 & D \end{pmatrix} Given A,D both diagonalizable (over F), and don't share any identical eigenvalues - Prove...

Given R\in M_n(F) and two matrices A\in M_{n1}(F) and D\in M_{n2}(F) where n1+n2=n R = \begin{pmatrix} A & B \\ 0 & D \end{pmatrix} Given A,D both diagonalizable (over F), and don't share any identical eigenvalues - show R is diagonalizable. I'm building eigenvectors for R, based on the...

Homework Statement Let ##O(3)## denote the set of all orthogonal 3 by 3 matrices, considered as a subspace of ##\mathbb{R}^9##. (a) Define a ##C^\infty## ##f:\mathbb{R}^9 \rightarrow \mathbb{R}^6## such that ##O(3)## is the solution set of the equation ##f(x) = 0##. (b) Show that ##O(3)## is a...

I am running a program that has to diagonalize large, complex Hermitian matrices (the largest they get is about 1000x1000). To diagonalize the matrix once isn't too bad, but I need to diagonalize thousands to millions of different Hermitian matrices each time I run a simulation. If I only need...

Part c) I'm not quite sure what to do, I've found the det(U) is 2, but no idea what this actually shows to be honest, any help?

Show that a rotation by θ followed by a rotation by φ can be expressed as either two consecutive rotations, or one rotation of (θ + φ). That is, show that Qθ Qφ = Qθ+φ, where Q is the rotation matrix. Can anyone answer this question I'm a beginner in Linear Algebra

Hey guys I hope I'm in the right place... I have this question I've been trying to solve for too long: Let A be an nxn matrix, rankA=1 , and n>1 . Prove that A is either nilpotent or diagonalizable. My best attempt was: if A is not diagonalizable then det(A)=0 then there is a k>0 such that A^k...

Hi all, Actually I'm supposed to run and find results in google search. But that doesn't give any useful information, retrieves some nomenclatures which deals with estimation of technique or deriving the stiffnesss mass matrices for 2D frame element. But I'm looking for 3D frame element with...

if you perform row operations on a matrix A to convert it to the identity matrix and then use the same row operations and apply it to another matrix B, why is it that the end result of B^r does not depends on B's actual sequence

For part b: Could anyone why it is + or - 3? I really don't understand why there would be two solutions as det|P| as it would just be the absolute value of P, meaning just +ve?

Do we know how we came up with the idea of matrices and determinants? How was the idea of solving linear equations using matrices and determiannts come up. I do not find it useful at all. Does anyone know a site which explains its history and usefulness?

Hi all. I'm having a little trouble in understanding precisely how to calculate reduced density matrices. No literature I've been able to get my hands on has made it clear how precisely to work out partial matrices. For example, if we have a bi-partite state for Alice's and Bob's particles...

saravananbs's question from Math Help Forum, Hi saravananbs, No. The converse is not true in general. Take the two matrices, \(A=\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}\mbox{ and }B=\begin{pmatrix}0 & 1\\1 & 0\end{pmatrix}\). \[\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}\begin{pmatrix}1 \\...

Hello, I'm new here and in matlab, so if I do mistakes, please, tell me. I'm working on my thesis and I need to extract some matrices and elements, but I can't write the for-loop exactly. For example, I have to read six matrices (but then I'll have more matrices) and this is too long matrix_1...

Homework Statement The Attempt at a Solution %2.11 x=1:0.5:5; a=sqrt(2.8); n=[1:1:100]; Sn=prod(1-(x.^2)./(n.^2-a^2)); S_inf=(a/sqrt(a^2+x.^2)).*sin(pi*sqrt(a^2+x.^2))/sin(pi*a); e_n=100*(Sn-S_inf)./S_inf I know I can't use ./ if the two matrices are different, meaning x./n. How...

http://dl.dropbox.com/u/33103477/prune.png I am unsure if the the answer is: {\begin{pmatrix} 2 & 1 \\ 5 & 1 \end{pmatrix}}, {\begin{pmatrix} 3 & -1 \\ 7 & 4 \end{pmatrix}} or {\begin{pmatrix} 2 & 1 \\ 5 & 1 \end{pmatrix}}, {\begin{pmatrix} 3 & -1 \\ 7 & 4 \end{pmatrix}}...

So, I was studying coupled oscillations and came across a statement that I couldn't figure out. It was that a particular matrix was symmetrical by Newton's Third Law. I know what Newton's Third Law is, I know what symmetric matrix is. But, for example, a matrix like this: -2k/m...

Homework Statement Let V be the vector space of all symmetric 2x2 matrices, and consider the bases. S = { [1 0] [0 1] [0 0] [0 0],[1 0],[0 1]} B = { [1 1] [-1 1] [1 0] [1 2],[ 1 1],[0 1]} of V. Find the transition matrix Ps,b. Use your answer to calculate Pb,s. Homework Equations a =...

Ok, first off I will admit that I really am pretty much ignorant of proper QM, as I am a first year undergraduate at a UK university. Today our lecturer, in the final lecture of a Vibrations and Waves course, demonstrated how the Schrodinger equation is derived from applying the Energy and...

Dear members, I have a rather silly question. As we all know only the compatible matrices can be multiplied. My derivation of some Finite Element formulation has, however, led me to the multiplication of two incompatible matrices. I was wondering if we could make these incompatible...

How can i find all matrix $A$ of order $2\times 2$ that satisfy the $A^2 = \begin{pmatrix}1 & 1\\ 0 & 1 \end{pmatrix}$

Dear forum members, I have a small problem counting all the invertible matrices of the size 2x2 providing \mathbb{Z}_{n}. This problem was difficult for me so I decided to go on counting how many invertible 2x2 matrices there are for n=32. My strategy to solve the problem was first by...

I thought I would ask this in the homework section. Homework Statement I should be able to write down the eigenvectors and eigenvalues of diagonal and triangular matrices on sight. M = \begin{bmatrix} 1 &0 \\[0.3em] 0 & x \\[0.3em]...

This isn't really a homework question, but it is relevant to heling me finish my homework. When you are diagonalizing a matrix, how do you know what order to put the eigenvectors in. One of my homework problems is with the eigenvalues 1, 2, and 4. [-1] [1] is the matrix corresponding to the...

If we take an nxn diagonal matrix, and multiply it by an nxn matrix C such that AC=CA, will C be diagonal? I know, for instance, if C is a matrix with ones in every entry, AC=CA holds. But is there a more general way to format such a counterexample, or have I already provided a sufficient...

The no. of $3 \times 3$ non - singular matrices matrices, with four entries as $1$ and all other entries as $0$

Does Sylvester's Criterion hold for infinite-dimensional matrices? Thanks!

Homework Statement I have a final coming up and I am a bit fuzzy on how to create a matrix that represents a rotation or reflection about a certain plane (in R3). Say we are given a rotation/reflection about either a plane or a line through two points T(v)=Av and we are told to find A. Do we...