Projection Definition and 409 Threads

Homework Statement Find the projection of the intersection between the two surfaces S1: z = 4-x^2 - y^2 and S2: 4x^2y = 1 (x>0) in the xy-plane 2. The attempt at a solution 4-x^2 - y^2 = 4x^2y -1 Is this all I need to do?

Image a kite (1 m wide, 3 m high, both crossing at a third of the height). Also imagine a digital camera (800x600 pixel with a horizontal field of view of 45°). After launching the kite a photo is taken with the camera. How can I easily calculate the exact position *and* rotation of the...

[SOLVED] Quick Question: Is this matrix an orthogonal projection? Homework Statement P=[0 0 ] [11] Homework Equations The Attempt at a Solution Its orthogonal if the null space and range are perpendicular. Range=[0 ] [x+y] null space=[x

Hi all Not sure if I posted in the right spot but my question is in regards to optics and projection. To make a little less confusing I will try to explain my dilemma. I have a triplet lens out of an old crt projector where the rear focal point is about 10mm form the rear lens surface. So...

Supposing we have a vector space V and a subspace V_1\subset V. Suppose further that we have two different direct sum decompositions of the total space V=V_1\oplus V_2 and V_1\oplus V_2'. Given the linear projection operators P_1, P_2, P_1', P_2' onto these decompositions, we have that...

Let X be a norm space, and X=Y+Z so that Y\cap Z=\{0\}. Let P:X->Z be the projection y+z\mapsto z, when y\in Y and z\in Z. I see, that if P is continuous, then Y must be closed, because Y=P^{-1}(\{0\}). Is the converse true? If Y is closed, does it make the projection continuous? If...

Problem: Let \vec{x} and \vec{y} be vectors in Rn and define p = \frac{x^Ty}{y^Ty}y and z = x - p (a) Show that \vec{p}\bot\vec{z}. Thus \vec{p} is the vector projection of x onto y; that is \vec{x} = \vec{p} + \vec{z}, where \vec{p} and \vec{z} are orthogonal components of \vec{x}...

[SOLVED] Hilbert space & orthogonal projection Homework Statement Let H be a real Hilbert space, C a closed convex non void subset of H, and a: H x H-->R be a continuous coercive bilinear form (i.e. (i) a is linear in both arguments (ii) There exists M \geq 0 such that |a(x,y)| \leq...

[SOLVED] Projection Theorem Homework Statement If M is a closed subspace of a Hilbert space H, let x be any element in H and y in M, then I have to show that \|x-y\| =\inf_{m\in M}\|x-m\| implies (equivalent to) that x-y\in M^{\perp} The Attempt at a Solution I have shown...

Are projections always continuous? If they are, is there simple way to prove it? If P:V->V is a projection, I can see that P(V) is a subspace, and restriction of P to this subspace is the identity, and it seems intuitively clear that vectors outside this subspace are always mapped to shorter...

[SOLVED] simple projectile motion.. Homework Statement A projectile is fired in such a way that its horizontal range is equal to 3 times its maximum height. What is the angle of projection? Homework Equations whole bunch for proj motion. The Attempt at a Solution I know that Dx =...

Projection of one vector on another?? Can anyone explain how to find the projection of one vector along another? I thought it was scalar (dot) product, but then I realized it WASN'T. What is this then? Anyone explain?

Homework Statement If at height of 40 m the direction of motion of a projectile makes an angle 45 degrees with the horizontal, then what is its initial velocity and angle of projection? Homework Equations The Attempt at a Solution

My teacher gave me this problem today and I have tried everything I know but I still haven't found the right answer. If anyone knows how to solve it, please share. Thanks At what projection angle will the range of a projectile equal its maximum height? Hint: 2 sin θ cos θ = sin 2 θ

Homework Statement How do I prove that if, |\vec{u_1}><\vec{u_1}| + |\vec{u_2}><\vec{u_2}| = I, where 'I' is the indentity matrix, that u_1 and u_2 are orthogonal and normalized? Can anybody get me started?

Golf problem... Ben is out at the practice range hitting golf balls. How much further will a golf ball with an initial speed of 75.0 m/s go when projected at 45.0 degree than when projected at 30.0 degree?

I noticed that it dosen't project to the origin of the plane from the north pole. However the projection describes it as mapping to the whole equitorial plane which is wrong! i.e take S^1 projecting to R. From the north pole the projection formula is y=-(x-a)/a however a can't be 0. So the...

Homework Statement 1.I have a vector defined by (v1,v2,v3). 2. I want to project this vector on a plane such that a point on that plane is defined by (p1,p2,p3).Also, the normal to the plane is given by (n1,n2,n3) 3.Can anyone help me to the projection of the vector on this plane...

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? Please help. Thanks.

Homework Statement A 6kg projectile is launced at an angle of 30 degrees to the horizontal and at initial spped of 40m/s. At the top of its flight, it explodes into 2 parts with masses 2 and 4 kg. The fragments move horizontally just after the explosion and the 2kg piece lands back at the...

I am studying for exam and something does not make sense anymore: looking at projection matrix, how come P=P2 where P2 = A(ATA)-1ATA(ATA)-1AT = A(ATA)-1AT = P but then they also say that cancelations (like distributing inverse operation and having AA-1 = I type things) are possible only if A...

Homework Statement I am trying to find the matrix M that projects a vector b into the left nullspace of A, aka the nullspace of A transpose. Homework Equations A = matrix A ^ T = A transpose A ^ -1 = inverse of A e = b - A x (hat) e = b-p I know that the matrix P that projects...

Homework Statement Let V=Mn(F) be the space of all nxn matrices over F; define TA=(1/2)(A+transpose(A)) for A in V. Verify that T is not only a linear operator on V, but is also a projection. Homework Equations A is a projection when A squared=A. The Attempt at a Solution I don't...

Homework Statement A stone of mass 2 kg is projected horizontally with a speed of 20 m/s from a cliff which is 15 m above the ground. Find the energy possessed by the stone just before touching the ground. A. 400J B. 500J C. 600J D. 700J Homework Equations The Attempt at a...

There is many projection (or measurement) postulates in quantum mechanics axioms: von Neumann measurement, Luders postulate... But does anybody know sth. about DIRAC POSTULATE? Thx

Hi all I have searched on google already but couldn't find any good tutorials. I am talking about isometric projection from area (3D) to coordinate system (2D). Here is the ''easy'' example of the little house in 3D view http://img.photobucket.com/albums/v309/Andreii/3d2d.jpg . I know I...

I'm wondering if the projection of the empty set has been defined? several books I've read seem to regard it in different ways

can anyone explain 1)first angle projection 2)third angle projection what are the advantages & disadvantages of the above why not use second and fourth angle.

After 10 years of teaching middle school, I am going back to grad school in math. I haven't seen Linear Algebra in more than a decade, but my first class is on Generalized Inverses of Matrices (what am I thinking?). I have a general "rememberance" understanding of most of the concepts we're...

I am having a difficult time with the motion equation when the problem only includes an X value and an angle. The problem is to fin the velease speed of the ball when a player makes a shot to a basket when he is 6.02 m from the basket and the basket is 2.05 m above the floor. The player is 2.05...

I looked, but I could not find an Aitoff projection of the constellations that is aligned with galaxial coordinates. Any help is appreciated, thanks!

Let T in L(V) be an idempotent linear operator on a finite dimensional inner product space. What does it mean for T to be "the orthogonal projection onto its image"?

A 1250 kg cannon, which fires a 55 kg shell with a speed of 566 m/s relative to the muzzle, is set at an elevation angle of 39° above the horizontal. The cannon is mounted on frictionless rails, so that it recoils freely. What is the speed of the shell with respect to the Earth...

"A 35 mm slide (picture actually 24*36 mm) is to be projected on a screen 1.8*2.7 m placed 9 m from the projector. What focal length lens should be used if the imageis to cover the screen?" I was trying to do this problem using the formula (1/do)+(1/di)=(1/f), but hten i realized i don't have...

I'm looking for a Mercanter projection of Mars that I can print out of my printer. Or even just a rectangle, where can I find one?

The problem reads as follows: "The projection of a point P = (x,y,z) to a plane is a point on the plane that is closest to P. If the plane is defined by a point P0 = (x0,y0,z0) and a normal vector n=(x1,y1,z1), computer the projection of P on this plane." Well, I haven't had a relevant...

In any book on differentiable manifolds, the stereographic projection map P from the n-Sphere to the (n-1)-plane is discussed as part of an example of how one might cover a sphere with an atlas. This is usually followed by a comment such as "it is obvious" or "it can be shown" that the inverse...

I know if a cirlce (on S^2) does not contain N (0,0,1) then it is mapped onto the plane H as a circle. Now say the circles on S^2 are lines of latitude. When mapped by the stereographic projection they are cirlces in R^3 on the plane H. Now the only thing I am not sure on is, my claim: When...

Someone asked me a basic physics question, and I'm not believing my answer, even though it appears to have the correct limiting behavior. This is driving me completely insane. Suppose I stand on a sidewalk, 10 feet from the middle of an infinitely long and straight road. I have a flashlight...

hi, i read lots of book regarding fictitious force - coriolis and centrifugal forces, but i am not clear how to determine the direction of the force.. example. if we throw a ball vertical up , how we can know the deviation from the original position ( from book we know that if the ball...

Hey Everyone, I have this question that's been giving me a hard time, I don't really know how to do it. "Let A be an arbitrary vector. It may be projected along a direction V on the plane P with normal vector n. What is its image A` ?" I know that A + lamda*V = A` , and that we have to...

I was copying my friends notes and had a hard time understanding one of the examples he had written down from lecture. See the attachment for a the picture of the example. This example looks like a projection of two vectors to me, but I'm not sure. u'=\frac{4i+2j}{\sqrt{20}} u' = unit...

Have there been any experiments designed to explicitly test the projection postulate? I mean that part of it that says the measured particle is left in an eigenstate of the measured operator. The usual devices for measuring particles (photomultipliers, phosphor screens, etc.) don't really...

Me again. I would really appreciate if you could help me with the following proof: a,b,c are vectors Does aproj.(b+c) =aproj.b + aproj.c Sorry for notation. Thank you.

The projection lens in a certain slide projector is a single thin lens. A slide 20.0 mm high is to be projected so that its image fills a screen 2.0 m high. The slide-to-screen distance is 3.00 m. (a) Determine the focal length of the projection lens. (b) How far from the slide should the...

Well, right now I'm working on one helluva a problem... Basically, a projectile is given a velocity of V sub "o" (Vo). The launch angle is gamma degrees above an surfaced which is inclined theta degrees above the horizontal. I'm tasked with finding its range along the inclined surface as well...

So I'm trying to prove that the map f(x,y,z) = \frac{(x,y)}{1-z} from the unit sphere S^2 to R^2 is injective by the usual means: f(x_1,y_1,z_1)=f(x_2,y_2,z_2) \Rightarrow (x_1,y_1,z_1)=(x_2,y_2,z_2) But i can't seem to show it... :frown: I end up with the result that...

Hey there I'm working on questions for a sample review for finals I'm stuck on these three I think I'm starting to confuse all the different theorem, I'm so lost please help 1) Find the coordinate vector of the polynomial p(x)=1+x+x^2 relative to the following basis of P2: p1=1+x...

Find the matrix A of the orthogonal projection onto the line L in R2 that consists of all scalar multiples of the vector [2 5]T . OK...I really don't know how to start off with this problem. If somehow could just help me out there I will try to muddle my way through the rest ! Thanks.

I'm trying to prove some stuff that involves the projection map, say p:X x Y ->X. But I need to know if it's continuous. If a map is continuous, then the preimage of a open/closed set is open/closed. The problem is, what do open sets in X x Y look like? I know what the basis elements are...