Projection Definition and 409 Threads

Homework Statement Let A be an n×n matrix which has the property that A^2 =A. (i) Write down the most general polynomial in AHomework EquationsThe Attempt at a Solution My biggest problem is that I don't even understand what the question is asking Is it just sum (alphaA^n)=0 but A^n=A...

Homework Statement I feel like this is a easy question but it seems the answer key doesn't seem to be right. So say I have 2 vectors and I'm trying to find the projection of vector u perpendicular to the vector v Homework EquationsThe Attempt at a Solution So I don't remember doing...

Hi all! I'm having problems understanding the operator algebra. Particularly in this case: Suppose I have this projection ## \langle \Phi_{1} | \hat{A} | \Phi_{2} \rangle ## where the ##\phi's ## have an orthonormal countable basis. If I do a state expansion on both sides then I suppose I'd get...

Washington Post: https://www.washingtonpost.com/news/morning-mix/wp/2016/03/21/study-these-are-the-u-s-cities-that-could-be-hit-by-a-zika-outbreak/ Study...

Homework Statement T: R^2 --> R^2 given as a projection on the line L = 5x+2y=0 decide matris T? Homework EquationsThe Attempt at a Solution L= 5,2 X=x1, x2 projL on X = (5x1+2x2)/29 *(5,2) = 1/29 [25 10 10 4] is this correct?

My textbook says: "if ## V = W_1 \oplus W_2 ##,, then a linear operator ## T ## on ##V ## is the projection on ##W_1## along ##W_2## if, whenever ## x = x_1 + x_2##, with ##x_1 \in W_1## and ##x_2 \in W_2##, we have ##T(x) = x_1##" It then goes on to say that "##T## is a projection if and only...

Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...

Hi everyone, i hope this is the right place to post this. Anyway, I'm creating a game, and I'm trying to calculate and project future car movement path based on steering angle of the wheels. By using equation: r = wheelbase / sin(steeringAngle) I'm able to calculate turning radius. But the...

Using a high-power LED light (the surface mount kind, about 4x4mm with 120 degree viewing angle) I'd like to project shadows of a fine metal mesh onto a wall. I have tried various lens arrangements and found that placing a pinhole in front of the LED makes the sharpest shadows. This makes...

Hi all, This is the problem I want to share with you. We have the hamiltonian H=aP+bm, which we are commuting with the position x and take: [x,H]=ia, (ħ=1) Ok. Now if we take, instead of x, the operator X=Π+ x Π+ +Π-xΠ- where Π± projects on states of positive or negative energy the...

I am working through some course notes where the aim is to derive the equations of motion satisfied by the left handed and right handed components of the Dirac spinor ##\psi##. From the Dirac lagrangian, we have $$\mathcal L = \bar \psi (i \not \partial P_L - m P_L)\psi_L + \bar \psi (i \not...

Many important techniques in fields such as CT and MR imaging in medicine, nondestructive testing and scientific visualization are based on trying to recover a matrix from its projections. A small version of the problem is given the sums of the rows and columns of a 2 x 2 matrix, determine the...

$$A$$ is a hermitian matrix with eigenvalues +1 and -1. Let $$\left|+\right>$$ and $$\left|-\right>$$ be the eigenvector of $$A$$ with respect to eigenvalue +1 and eigenvalue -1 respectively. Therefore, $$P_{+} = \left|+\right>\left<+\right|$$ is the projection matrix with respect to eigenvalue...

Homework Statement : The trajectory of a projectile in a vertical plane is y = √3 x - (1/5)x2, where x and y are respectively horizontal and vertical distances of the projectile from the point of projection. Find the angle of projection and speed of projection.[/B]Homework Equations ...

Homework Statement |-1/2 -sqrt(3)/2 | |sqrt(3)/2 -1/2 | Homework Equations I don't know The Attempt at a Solution Hey everyone, I've been asked to find the "orthogonal projection" on this matrix, this is part B to a...

Hi, In a 3D plane, I have another plane P1 equal to Ax+By+Cz=0 (D=0 since one of its points is (0,0,0) ) If I have the coordinates (x1,y1,z1) in the first plane, what are the cordinates of this point in the P1 plane? I know the equation of the intersection line. But my calculations are going...

In Celestial Mechanics the equation: LP = w + N (Longitude of the Perihelion = Argument of the Perihelion + Longitude of the Ascending Node) is confusing. Both "LP" and "N" are on the Ecliptic Plane but "w" is not. "w" is on the Elliptic Plane with a tilt of "i" Inclination from the Ecliptic...

Let r:R2 →R3 be given by the formula Compute the second fundamental form with respect to this basis (Hint: There’s a shortcut to computing the unit normal n). I can't find thi shortcut, does anyone help me? I'm solving it with normal vector and first and second derivate, but I obtained...

The book I am using for my Introduction to Topology course is Principles of Topology by Fred H. Croom. Problem: Prove that if ##X=X_1\times X_2## is a product space, then the first coordinate projection is a quotient map. What I understand: Let ##X## be a finite product space and ##...

Homework Statement Consider a symmetric n x n matrix ##A## with ##A^2=A##. Is the linear transformation ##T(\vec{x})=A\vec{x}## necessarily the orthogonal projection onto a subspace of ##R^n##? Homework Equations Symmetric matrix means ##A=A^T## An orthogonal projection matrix is given by...

It basically boils down to: show that: $$\int_{-\infty}^{\infty} dy \frac{J_1 \left ( \pi\sqrt{x^2+y^2} \right )}{\sqrt{x^2+y^2}} = \frac{2 \sin{\pi x}}{\pi x} $$ My life story (somewhat irrelevant): A jinc function is besselj(1,pi*r)/( 2r ), a sinc is sin(pi*x) / (pi*x) I have noticed, while...

Hello! First of all I want to say that I am not a physicist, but an artist currently doing my master thesis. I have been trying to build a solar powered slide projector. It works very simple – I reflect sunlight through a slide and enlarge it with a lens. My problem was that I wanted more...

I'm aware there have been plenty of discussions about Copenhagen interpretation vs ensemble interpretations (myself I have always been more fond of the latter) but I intend to explore new perspectives and stick as much as possible to what QM practitioners do in practice as opposed to obscure...

Homework Statement Watch the crash test video , and determine the following: 1. How fast is one of the crash test dummies thrown forward (the crash at :34 seconds) ? Pick either one, and be clear how you estimate this. 2. Assuming the speed you got from part (1), how high would a different...

Hey! :o To find the projection of $\overrightarrow{c}$ on $\overrightarrow{a}$ do we have to use the formula $$\frac{\overrightarrow{c} \cdot \overrightarrow{a}}{||\overrightarrow{a}||^2}\overrightarrow{a}$$ ?? (Wondering) For example, if we have $\overrightarrow{c} =(4, 2, -6)$ and...

Homework Statement [Imgur](http://i.imgur.com/VFT1haQ.png) Homework Equations reflection matrix = 2*projection matrix - Identity matrix The Attempt at a Solution Using the above equation, I get that B is the projection matrix and E is the reflection matrix. Can someone please verify if this...

Does anyone know where I might find WMAP and/or Planck maps of the dipole/quadrupole/octupole images that were done using the cartesian cylindrical projection? I've been able to find them in the standard Mollweide projection via Google images but can't seem to find any that were made with the...

I am working on a project where I have to project a logo on a very narrow angle like shown below: The projection distance will vary between 6-10 yards and at 10 yards the projected diameter will not be larger than 12inches so the beam angle needs to be less than 5 degrees. The idea is to...

I've attached the question to this post. The answer is false but why is it not considered the orthogonal projection? ## A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} ## ## B = \begin{bmatrix} x \\ y \end{bmatrix} ## ## AB =...

Suppose I have particle in three dimensional space whose position space wavefunction in spherical coordinates is ##\psi(r,\theta,\phi)##. The spherical harmonics ##Y_{\ell,m}## are a complete set of functions on the 2-sphere and so any function ##f(\theta,\phi)## can be expanded as...

Homework Statement Let ##G##, ##H##, and ##K## be groups with homomorphisms ##\sigma_1 : K \rightarrow G## and ##\sigma_2 : K \rightarrow H##. Does there exist a homomorphism ##f: K \rightarrow G \times H## such that ##\pi_G \circ f = \sigma_1## and ##\pi_H \circ f = \sigma_2##? Is this...

see figure: http://en.wikipedia.org/wiki/Vector_projection#mediaviewer/File:Projection_and_rejection.png Im reading about projections of vectors. My book says nothing about what the projection a1 of a on b is when a and b are complex vectors. To find the formula for the projection, one needs...

Homework Statement The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maximum height. What is the initial projection angle of the projectile? 2. The attempt at a solution First I tried to find the speed for the max height. vf2 - vi2 =...

I know that Space-Time is curved near the source of stress, but I'm not quite as clear what that means for the projection onto normal space and I'm trying to get my head around it. Is a kilometer on Mercury the same as a kilometer on Neptune? Is there a relatively simple formula (that is, an...

If we are given an operator, say in matrix or outer product form, then how can we check if it is a projection operator? Is idempotence a sufficient condition for an operator to be a projection operator or are there any other conditions?

Homework Statement In the real linear space C(-1, 1) with inner product (f, g) = integral(-1 to 1)[f(x)g(x)]dx, let f(x) = ex and find the linear polynomial g nearest to f. Homework EquationsThe Attempt at a Solution I understand that the best approximation for g is equal to the projection of...

This is a question from Altland and Simons book "Condensed Matter Field Theory". In the second exercise on page 64, the book claims that if we define \hat P_s, \hat P_d to be the operators that project onto the singly and doubly occupied subspaces respectively, then at half-filling the...

I was placed into honors calculus III for school. I was happy about this and I consider myself to be a pretty quick learner in math. However, my teacher is using many notations and terms that I am completely unfamiliar with. Mostly, I believe, because I've never taken linear algebra. I am...

Hi. I have a question about the Holographic Principle. I've been looking up things about it for a while now, and I think I understand it. The total content of a space is propositional to the area surrounding it and not the volume. The thing I'm having trouble with is how everything seems 3d...

Homework Statement Determine the magnitude of the projection of force F = 700N along the u axis. Homework Equations Cosθ = (A • B)/(||A|| * ||B||) The Attempt at a Solution I'm guessing I have to use the above equation, but my problem is finding the B vector. A is easy enough...

Homework Statement Let A be the 4x2 matrix |1/2 -1/2| |1/2 -1/2| |1/2 1/2| |1/2 1/2| Find the projection matrix P that projects vectors in R4 onto R(A) Homework Equations projSx = (x * u)u where S is a vector subspace and x is a vectorThe Attempt at a Solution v1 = (1/2, 1/2...

I've been reading Thomas Jordan's Linear Operators for Quantum Mechanics, and I am stalled out at the bottom of page 40. He has just defined the projection operator E(x) by E(x)(f(y)) = {f(y) if y≤x, or 0 if y>x.} Then he defines dE(x) as E(x)-E(x-ε) for ε>0 but smaller than the gap between...

Hello guys, I want to verify or rather show that a given matrix ##T## does represent a projection from ##\mathbb{R^{3}}## to a particular plane, also lying in ##\mathbb{R^{3}}##. Would it be enough to pre-multiply that matrix to an arbitrary vector ##(x,y,z)##, and see if the resulting...

If ##A## is not projection operator. Could ##A^k## be a projection operator where ##k## is even or odd degree. Thanks for the answer.

Hi, So, I am working through section 5.2 of Sakurai's book which is "Time Independent Perturbation Theory: The Degenerate Case", and I see a few equations I'm having some trouble reconciling with probably because of notation. These are equations 5.2.3, 5.2.4, 5.2.5 and 5.2.7. First, we...

Homework Statement This is an example problem where you have a force F at 100N applied at an angle of 45 degrees from a horizontal u-axis. You have the u-axis at zero degrees, then 45 degrees after that you have the Force then 15 degrees after th at you have the v-axis You are asked to...

A linear operator L:Rn→Rn is called a projection if L^2=L. A projection L is an orthogonal projection if ker L is orthogonal to L(Rn). I've shown that the only invertible projection is the identity map I_Rn by using function composition on the identity L2(v)=L. Question: Now suppose that L...

"Projection Using Dot Product" "Finding a Force" (Boat Problem) Homework Statement ------------------------------------------------------------------------------------------- A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down...

Homework Statement Hey guys. So here's the situation: Consider the Hilbert space H_{\frac{1}{2}}, which is spanned by the orthonormal kets |j,m_{j}> with j=\frac{1}{2}, m_{j}=(\frac{1}{2},-\frac{1}{2}). Let |+> = |\frac{1}{2}, \frac{1}{2}> and |->=|\frac{1}{2},-\frac{1}{2}>. Define the...

Okay, I thought that there would exist a projection from ##\mathbb{Z}^{p-1}## to ##\mathbb{Z}_{p}## where ##p## is a prime. Like there exist a projection from ##\mathbb{Z}## to ##\mathbb{Z}_p##