Projection Definition and 434 Threads

Typically I understand that projection operators are defined as P_-=\frac{1}{2}(1-\gamma^5) P_+=\frac{1}{2}(1+\gamma^5) where typically also the fifth gamma matrices are defined as \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 and.. as we choose different representations the projection...

Typically I understand that projection operators are defined as P_-=\frac{1}{2}(1-\gamma^5) P_+=\frac{1}{2}(1+\gamma^5) where typically also the fifth gamma matrices are defined as \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 and.. as we choose different representations the projection...

Homework Statement (firstly, Apologies for having to use a picture..) If u^{i} is the 4-velocity of a point on a manifold, then we use affine parameterisation g_{ij}u^{i}u^{j}=1. The attached picture shows our rest frame, ie x^{0}=const and a point ("us") on this surface. If our velocity is...

Note: * = direct sum Let P : V--> V me a linear map such that P^2 = P . Prove that V = N(P ) * R(P ). (Here V is not assumed to be finite dimensional.) Conversely, prove that if V = W1 * W2 then there exists a linear map P : V --> V with P^2 = P and N(P ) = W1; R(P ) = W2. Such P is called...

Homework Statement i have to find the scalar and vector projection of a=i-j+k and b=2i-j-2k and i got: Vector proj = (1/3)(i-j+k) = i/3 + j/3 + k/3 scalar proj = (1/9)(2i-j-2k) = 2i/9 - j/9 - 2k/9 is this correct?

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]...

Hi, I'm having trouble proving that a particular operator is a projection operator. If you could take a look at the attached document, that contains my question I'd be really grateful!

Homework Statement The fireman wishes to direct the flow of water from his hose to the fire at B. Determine two possible angles θ1 and θ2 at which this can be done. Water flows from the hose at v = 55 ft/s. There is no air friction. Homework Equations v = v0 + at x = x0 + vt v2 = v^{2}_{0}...

A body is projected from ground level with a speed of 24 m/s at an angle of 30 degrees above the horizontal. Neglect air resistance and take gravity to be 10 m/s. Calculate: a) The time taken to reach its highest point b) The greatest height reached c) The horizontal range of the body a)...

Homework Statement I want to understand the proof of proposition 7.1 in Conway. The theorem says that if \{P_i|i\in I\} is a family of projection operators, and P_i is orthogonal to P_j when i\neq j, then for any x in a Hilbert space H, \sum_{i\in I}P_ix=Px where P is the projection...

Homework Statement Hi I have been stumped by this question for the past few days. Worrying since I will be sitting STEP in June! Never mind. It goes like this: A particle is projected vertically upwards with a speed of 30m/s from a point A. The point B is h metres above A. The particle moves...

Homework Statement A projectile is fired in such a way that that its horizontal range is three times its maximum height. What is the angle of projection? Homework Equations R = Vo2sin(2theta)/g H = (Vosin(theta)2/2g R = 3H Cancel Voo, g and sin(theta) to leave 4/3 tan(theta) =...

A golf ball with an initial speed of 91.1 m/s lands exactly 186 m downrange on a level course. The acceleration of gravity is 9.8 m/s2 . A)Neglecting air friction, what minimum pro- jection angle would achieve this result? Answer 6.35 minimum angle B)Neglecting air friction, what...

Homework Statement Hi, I got tied up with something.. I have a question that says if a projection P satisfies || P v || <= || v || then P is an orthogonal projection.. but if I drew in |R^2, a x-axis and a y=x line, and projected some vector onto the y = x line.. I still get || Pv || <=...

Homework Statement A person starts at coordinates (-2, 3) and arrived at coordinates (0, 6). If he began walking in the direction of the vector v=3i+2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn. Homework...

I am computing a stereographic projection in R^4 and i think i am correct in setting x=rcos(x)sin(y) y=rsin(x)sin(y) z=rcos(y) but can't see how to compute r as I do not know to visualise it graphically as was possible in R^3, any help would be greatly appreciated

I need to find the components of the force along AB along AC. So I got unit vectors for each like so: \vec{AB}=<-1.5,-3,1> \vec{AC}=<-1.5,-3,3> Norm AB=sqrt(12.25). Norm AC=sqrt(20.25). Then after multiplying the unit vector AB by the force I tried using the vector projection...

Homework Statement hello, I need help with projection of a rigid body with moment of inertia I, the rigid body was earlier moving on a circle of R radius with \omega angular velocity and was making angle of \alpha when centripetal force stopped to work. And I need to know if this rigid body...

Homework Statement Say you have two tables, S(A,B) , R(A,B), where A is the key for both. Lets say there is a tuple x0,y1 in S, and a tuple x0,y2 in R You use then this projection π(S\cupR) My question is,do the rules of primary key constraints apply to a projection? Will the result...

The Projv(x) = A(ATA)-1ATx I'm puzzled why this equation doesn't reduce to Projv(x) = IIx since (ATA)-1 = A-1(AT)-1 so that should mean that A(ATA)-1AT = AA-1(AT)-1AT = II What is wrong with my reasoning? Thanks.

Homework Statement Calculate the parallel projection on an infinite object defined by: f(x,y) = cos(2pi(2x+y)) from the angle phi = 45 degrees. Hint: Use the Central Slice Theorem and Fourier Transform (FT) of f(x,y). 2nd Hint: On a 2D image in Fourier space, delta functions are...

Hello, if we consider the stereographic projection \mathcal{S}^2\rightarrow \mathbb{R}^2 given in the form: (X,Y) = \left( \frac{x}{1-z} , \frac{y}{1-z} \right) how can I find the metric in X,Y coordinates? -- Should I first express the projection in spherical coordinates, then find...

Hello, Is there such a thing as a projection screen that is transparent to IR? I need to project an image onto a screen (rear-projection), but I also need to send an IR signal through the screen from the side of the human user back to the side with the projector. I think there are...

Homework Statement Show that the map f : R--> S1 given by f(t) =[(t^2-1)/(t^2+1), 2t/(t^2+1)] is a homeomorphism onto S1-{(1, 0)}, where S1 is the unit circle in the plane. I know this is a stereographic projection, but I do not know how to show that it has a continuous inverse. I am...

I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly the same map distance as 10 degrees of latitude at the Arctic Circle. As a disqualified example, the Mercator Projection has map distance increasing with increasing latitude...

Hi guys, I recently read some stuff about satellites in space being able to project 3D images on to the sodium layer of our atmosphere about 60 miles above the Earth. Is this possible? Can the sodium layer potentially be used as a giant movie screen for projections? The stuff i read was about...

1. Homework Statement The speed of projectile when it reaches its maximum height is one it half speed when it’s half maximum height. What is initial projection angle of the projectile? 2. Homework Equations I know it has been asked several times but no one give the answer with...

Hey PhysicsForums. Long time reader looking for some assistance Homework Statement [PLAIN]http://img205.imageshack.us/img205/3923/physicsg.jpg 2. The attempt at a solution I'm pretty sure the idea is to find the unit position vector to point A, and the force vector F. I found...

Homework Statement Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) . Homework Equations The Attempt at a Solution What I've tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar...

Homework Statement If a = <3,0,-1> find the vector b such that compaB = 2 Homework Equations None. The Attempt at a Solution |a| =\sqrt{3^2 + 1^2} = \sqrt{10} compaB = \frac{ a\cdot b}{|a|} 2 = \frac{3(b1) - 1(b3)}{\sqrt{10}} 2\sqrt{10} = 3(b1) - 1(b3) I don't know...

For a game I am thinking about making I would need to know how to project points from a differentiable bounded 3-manifold to a Euclidean plane (the computer screen). The manifold would be made from a 3-dimensional space with two balls cut out of it and a hypercylinder glued onto it at the holes...

Homework Statement I have a fixed unitary matrix, say X_d \in\mathfrak U(N) and a skew Hermitian matrix H \in \mathfrak u(N) . Consider the trace-inner product [tex] \langle A,B \rangle = \text{Tr}[A^\dagger B ] [/itex] where the dagger is the Hermitian transpose. I'm trying to find the...

Hi, Suppose I have a space X with coordinates (x,y,z) and a space Y with coordinates (x,y,z,t), so that dim(Y)=dim(X)+1. What is the difference between the projection (x,y,z,t)->(x,y,z) and the inclusion (x,y,z)->(x,y,z,t)? Are they each others inverses? Especially if x=x(t), y=y(t) and...

I see lots of references to time being the fourth dimension as well as there being 3 + 1 dimensions to spacetime as we know it, etc. I also see that time has to be treated differently in some of the constructs of physics. So it seems that time seems to be both similar and dissimilar to the other...

So basically I want to write some code in Python to project the movement of the moon and sun across the night sky. Basically, I need a projection such that the shape of the moon won't change as it moves in the sky (especially when it's near the horizon) - the objects have to look fairly good...

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 triangle in the plane z=1/2y with vertices (2,0,0) (0,2,1) (0,0,0) please help me to find out the projection of the triangle in xy plane. thanks Homework Equations The Attempt at a Solution

Homework Statement That is the question. The answer on the bottom is incorrect Homework Equations I believe that is the formula that is supposed to be used. The Attempt at a Solution All I really did was plug in the equation into the formula but there is something I am...

Hey, here is the formal question. M is a riemannian sub-manifold in N. a,b are vector fields such that for each p\inM, ap,bp \in TpM \subset TpN prove \nablaMba = pr(\nablaNba) where pr is the projection funtion pr:TpN\rightarrowTpM and \nablaN and \nablaM are the covariant derivative...

hi, so this is actually for a program I'm writing, but it's definitely more of a math question than a programming question. basically, i have an object that gets detected by a webcam attached to a computer. the object is just a piece of paper with a pattern on it, so it is, for the purpose of...

Suppose I had a plane and for whatever reason, I chose two non-orthogonal vectors in R3 to define that plane (they define a basis for the plane?). Suppose I have another vector in that plane. How do I find the (contravariant?) coordinates of another arbitrary vector in that plane? All I want...

Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...

Particle projection, momentum. Somewhat urgent. Homework Statement I didn't properly explain myself last time. I've included a diagram for reference. Two particle of masses m and 3m are connected by a light rigid rod. The system rests on a smooth horizontal table, the heavier mass due east...

I was just wondering where or if the brain projects mental pictures. I see them in front of my forehead. Is there where everyone sees them or is it different for everyone?

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.

Let S be a subspace of R3 spanned by u2=\left[ \begin{array} {c} \frac{2}{3} \\ \frac{2}{3} \\ \frac{1}{3} \end{array} \right] and u3=\left[ \begin{array} {c} \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}} \\ 0 \end{array} \right]. Let x=\left[ \begin{array} {c} 1 \\ 2 \\ 2 \end{array} \right]...

Hi everybody, Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light. For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of...

I'm an undergraduate computer-science student doing research in the field of computer vision, and one of the tasks I've been charged with is calibrating the camera on a robot. I understand the basic principles at work: a vector in 3D world coordinates is transformed into homogeneous 2-space...

Hi, in questions involving lenses, when using the "thin lens formulae" if my di is negative doesn't that mean the image is on the other side of the lens? in this example however it doesn't seem this holds true.. A doctor examines a patient's skin lesion with a 15 cm focal length...

D(g) is a representaiton of a group denoted by g. The representaion is recucible if it has an invariant subspace, which means that the action of any D(g) on any vector in the subspace is still in the subspace. In terms of a projection operator P onto the subspace this condition can be written...