Orthogonal Definition and 560 Threads

Find a polynomial that is orthogonal to f(x)=x2-1/2 using L2[0,1]. I have looked all in the textbook and all over the internet and have found some hints if the interval is [-1,1], but still do not even know where to start here. I think I was gone the day our professor taught this because I do...

Homework Statement first the question asks find the jacobian matrix of (ucosv) (usinv ) ( w ) i have the matrix ( cos(v) , -usin(v) , 0) ( sin(v) , ucos(v) , 0) ( 0 , 0 , 1) the question asks to show that the columns are orthogonal...

Homework Statement Let A be the matrix of an orthogonal projection. Find A^2 in two ways: a. Geometrically. (consider what happens when you apply an orthogonal projection twice) b. By computation, using the formula: matrix of orthogonal projection onto V = QQ^T, where Q = [u1 ... um]...

Hey guys, I have searched all over the forum but each thread seems to have a different way of solving this problem. I have changed the values from the coursework question so I can work it out for myself so here is an example one, I hope someone can give me some advice/steps on...

Let W1 and W2 be subspaces of an inner product space V with W1\subseteqW2. Show that (the orthogonal complement denoted by \bot) W2^\bot\subseteqW1^\bot.

Homework Statement Suppose we have a spin 1/2 Particle in a prepared state: \left|\Psi\right\rangle = \alpha \left|\uparrow\right\rangle + \beta\left|\downarrow\right\rangle where \left|\uparrow\right\rangle \left|\downarrow\right\rangle are orthonormal staes representing spin up and...

Really stuck... computing orthogonal complement? Homework Statement The Attempt at a Solution :cry: I'm really sorry I can't provide much here because I really don't know how to proceed. Could anyone offer a hint to get me started?

Homework Statement See figure attached for problem statement as well as my attempt. Homework Equations The Attempt at a Solution I can't see how we are expected to solve for 2 unknowns with only one equation? What am I missing? Am I supposed to simply define a in terms of b...

Hi All, I have a rigidbody simulation and I'm trying to calculate the local angular velocity of the object using the derivative of it's orthogonal rotation matrix. This is where I'm stuck as I haven't been able to find an example on calculating the time derivative from two matrices at t=n and...

Homework Statement Orthogonal matrix means Q^{T}Q=I, but not necessary QQ^{T}=I, so why can we say the inverse of Q is Q^{T}? Homework Equations The Attempt at a Solution the attempt is actually in my question. It's something i don't understand when doing revision.

1. The problem statement let \vec x and \vec y be linearly independent vectors in R^n and let S=\text{span}(\vect x, \vect y). Define the matrix A as A=\vec x \vec y^T + \vec y \vec x^T. Show that N(A)=S^{\bot}. 2.equations I have a theorem that says N(A) = R(A^T)^{\bot}. A is symmetric; A...

Homework Statement L1 pass through the points (-2,36,9) and (-8,44,12) L2 pass through the points (55,-31,7) and (41,-16,13) Find a point P on L1 and a point Q on L2 so that the vector \vec{}PQ is orthgonal to both lines. Homework Equations Dot product/ Cross product The Attempt at a...

Hi, I am working through the Feynman lectures on physics and trying to calculate the moment of inertia stated in the title. (the taxis of rotation going through c.m., orthogonal to length). My approach is to slice the cylinder into thin rods along the length, using the parallel taxis theorem...

Homework Statement Construct a third vector which is orthogonal to the following pair and normalize all three vectors: \underline{a}=(1-i,1,3i), \underline{b}=(1+2i,2,1) Homework Equations \underline{c}.\underline{a}=0 and \underline{c}.\underline{b}=0 where c=(x y z) The Attempt...

Homework Statement Find the orthogonal trajectories of the circles x2 + y2 - ay = 0The Attempt at a Solution I differentiated the equation w.r.t. x., Replaced dy/dx with -dx/dy, Solved the equation and got xyC = y2 - x2, where C is a constant. I did not eliminate 'a' after differentiating...

Diff Eq's -- orthogonal polynomials [PLAIN]http://img27.imageshack.us/img27/566/39985815.jpg I managed to do the first part, stuck in the part circled. Any help will be appreciated, thanks.

Homework Statement Find the orthogonal projection of the given vector on the given subspace W of the inner product space V? V=R3, u = (2,1,3), and W = {(x,y,z): x + 3y - 2z = 0} I don't understand how to find the orthonormal basis for W? Homework Equations I don't understand how to...

Homework Statement I am part way done with this problem... I don't know how to solve part e or part f. Any help or clues would be greatly appreciated. I have been trying to figure this out for a couple days now. W={<x,y,z>, x+y+z=0} is a plane and T is the orthogonal projection on it. a)...

Homework Statement Let U be a subspace of R4 and let S={x1, x2, x3} be an orthogonal basis of U. Given x1, x2, x3, find a basis for Uperp (the subspace containing all vectors orthogonal to all vectors in U). I am actually given three vectors x1, x2, x3, but I am looking more to...

Dear all, I have a matrix, namely A. I calculate its eigenvalues by MATLAB and all of its eigenvalues lie on the unit circle(their amplitudes equal to 1). But A is not an orthogonal matrix (transpose(A) is not equal to inverse(A) ). What other condition or relationship may be correct for it?

Homework Statement Say functions f and g continuous on [a,b] and happen to be orthogonal with respect to the weight function 1. Show that f or g has to vanish within (a,b). Homework Equations f and g are orthogonal w.r.t. a weight function w(x) if the integral from [a,b] of f(x)g(x)w(x)dx = 0...

Homework Statement A member of the family of the circles that cuts all the members of the family of circles x^2 + y^2 + 2gx + c=0 orthogonally, where c is a constant and g is a parameter is? Homework Equations The Attempt at a Solution Let the equation of the required circle...

Homework Statement Here is a picture of the problem: http://img84.imageshack.us/img84/1845/screenshot20100927at111.png If the link does not work, the problem basically asks: Let "a" be a non-zero vector in R^n. Let S be the set of all orthogonal vectors to "a" in R^n. I.e., a•x = 0 (where •...

First, let me start by apologizing for the length of this post. i do in fact have a question about a problem that i couldn't solve (at least not the way i wanted to solve it), but first there is a fair amount of foreground information i must lay down...beyond this foreground information, this...

Homework Statement Show that B|A| + A|B| and A|B| - B|A| are orthogonal. Homework Equations Orthogonal meaning at right angles

Yesterday I thought of a math problem, and it seems very simple, as I assume the solution is, and I want to know the answer more than I want to figure it out myself. Ok imagine point A and point B. The shortest path from A to B is a straight line. Let's now go from A to B in two orthogonal...

Hi I have two (two dimentional) linear equations (in the plane). and i am required to find out the angle between them. I have found the solution somewhere. the solution uses two vectors orthogal to the two lines. The problem now i have is: How to determine those orthogonal vectors? e.g: two...

I have a trivial question: Let assume a world sheet of a time-like spherical shell in Minkowski space-time. On the 2D-Minkowski diagram (R,T), where R is the radius and T is the time, the world line is represented by a time-like curve. Let assume that the shell collapse and its 4-velocity is...

Hey, I have a linear algebra exam tomorrow and am finding it hard to figure out how to calculate an orthogonal projection onto a subspace. Here is the actual question type i am stuck on: I have spent ages searching the depths of google and other such places for a solution but with no...

Homework Statement y=[4 8 1]^T u_1 = [2/3 1/3 2/3]^T u_2=[-2/3 2/3 1/3]^T Part 1: Write y as the sum of a vector y hat in W and a vector z in W complement Part 2: Describe the geometric relationship between the plane W in R^3 and the vectors y hat and z from the part above...

Hey all, I'm trying to find an orthogonal complement (under the standard inner product) to a space, and I think I've found the result mathematically. Unfortunately, when I apply the result to a toy example it seems to fail. Assume that A \in M_{m\times n}(\mathbb R^n), y \in \mathbb R^n and...

Homework Statement If {aj} and {bj} are two separate sets of orthonormal basis sets, and are related by ai = \sumjnAijbj Show that A is an orthogonal matrix Homework Equations Provided above. The Attempt at a Solution Too much latex needed to show what I tried...

Two vectors u,v ∈ V are said to be orthogonal if <u,v> = 0. Given the following statement: Two vectors u,v ∈ V are said to be orthogonal if <u,v> = 0. Is it correct to write it as: if <u,v> = 0, then the two vectors u,v ∈ V are said to be orthogonal or Is it correct to write it as...

Homework Statement Consider the vector V= [1 2 3 4]' in R4, find a basis of the subspace of R4 consisting of all vectors perpendicular to V. Homework Equations I mean, I'm just completely stumped by this one. I know that in R2, any V can be broken down to VParallel + VPerp, which...

Hey, I just fnished med school and I have been conduction biomechanical research for the past 3 years now. I am currently working on a project plan and I am encountering the following problem: We would like to measure compression across a joint, using partially threaded screws. For the...

Homework Statement Lets say I fix 3 mutually orthogonal unit vectors i, j and k. Consider an orthogonal transformation F of vectors defined by F(a_1i+ a_2j + a_3k)=a_1'i+a_2'k+a_3'k where \left( \begin{array}{ccc} a_1 \\ a_2 \\ a_3\end{array}\right) = A\left( \begin{array}{ccc} a_1' \\...

in this book I have by G.L Squires. One of the questions is: if \phi1 and \phi2 are normalized eigenfunctions corresponding to the same eigenvalue. If: \int\phi1*\phi2 d\tau = d where d is real, find normalized linear combinations of \phi1 and \phi 2 that are orthogonal to a) \phi 1 b)...

Hello, I guess this is a basic question. Let´s say that If I am given a matrix X it is possible to form a symmetric matrix by computing X+X^{T} . But how can I form a matrix which is both symmetric and orthogonal? That is: M=M^{T}=M^{-1}.

This start out as homework but my question is not about helping me solving the problem but instead I get conflicting answers depend on what way I approach the problem and no way to resolve. I know the answer. I am not going to even present the original question, instead just the part that I have...

Homework Statement A= [1 -1 0] [-1 2 -1] [0 -1 1] find orthogonal matrix P and diagonal matrix D such that P' A P = D Homework Equations The Attempt at a Solution i got eigenvalues are 0, 1, 3 which make D=[0 0 0; 0 1 0; 0 0 3] how to find P. because in...

Hey, I'm going over the Gram Schmidt method, and need some help understanding it. I understand that you're intending to create an orthogonal vector (i'll call them v) set based on a set of vectors you already have (i'll call them u). Then: Let v1 = u1 Now, construct the second orthogonal...

Homework Statement [PLAIN]http://img504.imageshack.us/img504/4985/capturewm.jpg Homework Equations N/A The Attempt at a Solution This is more of a conceptual question so I need a little help knowing what kinds of things to look for.

If x is ⊥ u and v, then x is ⊥ u - v. I know this is true because u - v is in the same place as u and v; therefore, x is orthogonal. How can this be written better?

Let S be the subspace of R^3 spanned by x=(1,-1,1)^T. Find a basis for the orthogonal complement of S. I don't even know where to start... I would appreciate your help!

(Note: this isn't a homework question, I'm reviewing and I think the textbook is wrong.) I'm working through the Gram-Schmidt process in my textbook, and at the end of every chapter it starts the problem set with a series of true or false questions. One statement is: -Every orthogonal set...

Homework Statement Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3? Homework Equations I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then... (x1)^T*x2=0 (x2)^T*x3=0...

Homework Statement Prove that [P]^2=[P] (that the matrix is idempotent) Homework Equations The Attempt at a Solution A(A^T*A)^-1 A^T= (A(A^T*A)^-1 A^T)^2 Where A^T is the transpose of A. I have no idea.

Find an orthogonal matrix whose first row is (1/3,2/3,2/3) I know orthogonal matrix A satisfies A*A' = I, where A' is the transpose of A and I is identity matrix. Let A = 1/3*{{1,2,3},{a,b,c},{d,e,f}} where a,b,c,d,e,f elements of R A'= 1/3*{{1,a,d},{2,b,e},{2,c,f}} We can obtain...

Homework Statement Let T: Rn -> Rn be a linear transformation, and let B be an orthonormal basis for R^n. Prove that [ the length of T(x) ] = [ the length of x ] if and only if [T]B (the B-matrix for T) is an orthogonal matrix. Homework Equations None I don't think. The Attempt at...

Homework Statement I have to find an orthogonal matrix with an eigenvalue that does not equal 1 or -1. That's it. I'm completely stumped. Homework Equations An orthogonal matrix is defined as a matrix whose columns are an orthonormal basis, that is they are all orthogonal to each other...