Projection Definition and 409 Threads

Another question I have from Schutz (CH3, 31 (c)), where he defines the Projection tensor as P_{\vec{q}}=g+\frac{\vec{q} \otimes \vec{q}}{\vec{q} \cdot \vec{q}} This can be written in component form (or rather the associated (1 1) tensor can after operating a few times on it with the metric)...

Homework Statement I have a vector diagram attached below. Vector A is perpendicular to vector B. How do you figure out what angle to use in order to project vector A onto the x and y axis? Homework Equations A dot B = ABcos(angle) The Attempt at a Solution 180-30-90 = 60?

Homework Statement A boy is standing on the peak of a hill (downhill), and throws a rock, at what angle from himself to the horizontal should he throw the rock in order for it to travel the greatest distance. Answer clues: 1. if, the angle from the slope to the horizontal = 60, then the...

Can anyone tell me what Orthagonal Projection means. I know the formula is b - proj b onto a. What does it mean exactly, I tried searching on google.

Homework Statement If an arbitrary intial state function for a particle in a box is expanded in the discrete series of eigenstates of the Hamiltonian relevant to the box configuration, one obtains: \psi(x,0) = \Sigma^{\infty}_{n=1}b_{n}(0)\varphi_{n}(x) If the particle is free, we obtain...

Homework Statement Is it possible for projuv=projvu Homework Equations The Attempt at a Solution This can only occur if: \frac{|\mathbf{u\cdot v}|}{^{\|u\|^{2}}}\mathbf{u} = \frac{|\mathbf{u\cdot v}|}{^{\|v\|^{2}}}\mathbf{v} So if either is the zero vector, it is...

Hi I was wondering if someone can explain what projection of vectors and scalars mean. I read a lot of site but they fail to give me a clear explanation. Thanks.

Homework Statement Given rank(R) and a QR factorization A = QR, what is the rank(A) Homework Equations The Attempt at a Solution I want to know if multiplication by a full rank orthonormal matrix Q and an upper trapezoidal matrix R yields rank(R)=rank(Q*R)=rank(A) This is...

Homework Statement A ball is projected horizontally from the edge of a table that is 0.443 m high, and it strikes the floor at a point 1.84 m from the base of the table. The acceleration of gravity is 9.8 m/s^2 Homework Equations a) What is the initial speed of the ball? Answer in...

A bit about optics. I was wondering what is the film (slide, or motion picture) projector with the widest projection angle. What are the current limitations?

i have to answer this question for an assignment that I need to do for mechanics. I am really really stuck - would somebody please mind helping... A ball thrown at an angle α to the horizontal just clears a wall. The horizontal and vertical distances to the top of the wall are X and Z...

I know that P = A(ATA)-1AT for a projection matrix. I was just wanting to know how to describe the matrix A as general as possible. For example do the columns and rows of A have to be linearly independant? Also I know that P = BBT is the projection matrix but how could I describe B as well.

I am trying to prove that the bth projection map Pb:\PiXa --> Xb is both continuous and open. I have already done the problem but I would like to check it. 1) Continuity: Consider an open set Ub in Xb, then Pb-1(Ub) is an element of the base for the Tychonoff topology on \PiXa. Thus, Pb is...

Homework Statement Suppose P ∈ L(V) is such that P2 = P. Prove that P is an orthogonal projection if and only if P is self-adjoint.Homework Equations The Attempt at a Solution Let v be a vector in V. Let w be a vector in W and u be a vector in U and let U and W be subspaces of V where dim W+dim...

I apologize for the excessive use of Latex, but for this particular problem I think the notation would be extremely difficult to read otherwise. I usually try to keep my use of Latex to a minimum. Homework Statement \text{Let } \mathbb{C}^3 \text{ be equipped with the standard inner product...

Hi there, I am trying to plot the coordinates of Supernovae onto what I think is known as a hammer plot i.e a 2D plot representing the surface of a sphere. I have no idea how to do this, and have been searching the internet to no avail. Can anyone offer any advice ? I only have a basic...

Homework Statement Let P\inL(V). If P^2=P, and llPvll<=llvll, prove that P is an orthogonal projection.Homework Equations The Attempt at a Solution I think that regarding llPvll<=llvll is redundant. For example, consider P^2=P and let v be a vector in V. Doesn't P^2=P kind of give it away by...

I am looking for good reading material and references on something. I have tried the google route and can't find anything so I thought I would ask the community of people who know... I want to learn more about the following scenario: Suppose I start with a 1 dimensional complex space. I want...

I am looking for good reading material and references on something. I have tried the google route and can't find anything so I thought I would ask the community of people who know... I want to learn more about the following scenario: Suppose I start with a 1 dimensional complex space. I...

Homework Statement Let A be a m x n matrix of rank n and let \textbf{b} \in R^{m}. If Q and R are the matrices derived from applying the Gram-Schmidt process to the column vectors of A and p = c1q1 + c2q2 + ... + cnqn is the projection of b onto R(A), then show that: a) c = QTb b) p...

hi, i want to display into IDL a mollview projection of the output fits file ('test_scalCls.fits') of CAMB program (Code for Anisotropies in the Microwave Background) but can't get it. I have IDL ASTRO, Healpix_2.11c and WMAP librairies and i tried several things: 1*/ HIDL>...

Draw a circle in a paper, if the line of sight perpendular to the paper , we see a circle ,but if the line of sight is not perpendular to the paper, must we see an ellipse ? how to prove it ? how to find out the major axis or minor axis ? It seem that when we observe the circle ,it should be...

I cannot visualise an oblique projection. I understood the orthogonal one: The orthogonal projection is P=U\cdotU*, where U is an orthonormal matrix (basis of a subspace) : U*\cdotU=I . Now the projection of matrix A on U vectors is: PA=U*\cdotA\cdotU . For the orthogonal projection, for a...

If i were to say: Map vector A onto line l would that mean the projection of A onto l or the rotation of A onto l?

I have an assignment question to find an equation of the orthogonal projection onto the XY plane of the curve of intersection of twp particular functions. If some one knows of a good web page that might explain this to me I would be greatly appreciate it. regards Brendan

I got this today as a take home bonus after a grade 12 physics test on kinematics and dynamics. QUESTION: Han Solo is holding a rope that is supporting Princess Leia, of mass 55 alistones (an alien unit of mass), 3 zons (an alien unit of length) above the ground as shown. Han, of mass 80...

Homework Statement Two math students erect a sun shade on the beach. The shade is 1.5 m tall, 2 m wide, and makes an angle of 60° with the ground. What is the area of shade that the students have to sit in at 12 noon (that is, what is the projection of the shade onto the ground)? (Assume the...

Homework Statement How would I prove this projection? I attached the equation. Homework Equations See attached equation. The Attempt at a Solution I tried using the formula with numbers but I didn't get to prove the equation. Any help would greatly appreciated. Thanks

Homework Statement Two math students erect a sun shade on the beach. The shade is 1.5 m tall, 2 m wide, and makes an angle of 60° with the ground. What is the area of shade that the students have to sit in at 12 noon (that is, what is the projection of the shade onto the ground)? (Assume the...

Out of the unit matrix and a real non-invertible symmetric matrix of the same size, \delta_{ij} and M_{ij} I need to build a set of projection matrices, A_{ij} and B_{ij} which satisfy orthonormality: A_{ij} B_{jk}=0, and A_{ij} A_{jk}=B_{ij} B_{jk}=\delta_{ik} Is this possible...

I've got this Toshiba 42H82 TV that the cat dragged in. Attached is a quick rough pic of what it's doing. I know it's difficult (and potentially dangerous) to repair a TV and wouldn't attempt to do it without a friend who knows his electronic repairs. Can this kind of thing be repaired? Ideas?

Hey everyone! I have a question regarding the matrix representation of a projection operator. Specifically, does the wavefunction have to be normalized before determining the projection operator? For example: |Ψ1> = 1/3|u1> + i/3|u2> + 1/3|u3> |Ψ2> = 1/3|u1> + i/3|u3> Ψ1 is obviously...

Hi all: I am confused about why photon only has two projection along the z-direction. This confusion came from what I read in shankar "printciple of quantum mechanics". In the chapter of field quantization, he explain that because photon must satisfy transverse condition. wave function...

please can u do this sum for me...really urgent situation find the equation of the orthogonal projection of the line x+1/1 = 2y/-1 = z+1/2 on the plane x+2y+z=12 thanks in advance

A force F of 6 units acts in the direction 30 degrees west of north. An object is constrained to move north-westerly, that is, 45 degrees west of north. (a) Sketch the force vector roughly to scale on a set of axes that has the positive y axis pointing north, and write F using exact values...

Stereographic Projection for "general" surfaces First off, sorry if this is in the wrong forum. I came across this while studying computer vision, but it's of a somewhat mathematical nature. Please move it if it's in the wrong place. In the book I'm reading*, stereographic projection is used...

Is a projection a quotient map? I think a quotient map is an onto map p:X-->Y (where X and Y are topological spaces) such that U is open/closed in Y iff (p)-1(U) is open/closed in X. And a projection is a map f:X-->X/~ defined by f(x)=[x] where [x] is the equivalent class (for a...

let pf(x)= sum( from i=1 to k) <x, ui>ui, show pf is a projection. Ive tried to show this fact myself but i failed. Please some one help me out. thanks Note ui = u1...un an orthogonal basis of V where V is a vector space.

Find the matrices of the transformations T which orthogonally project a point (x,y,z) on to the following subspaces of R^3. (a) The z-axis (b) the straight line x=y=2z (c) the plane x+y+z=0 (a) is easy just the matrix [0 0 0;0 0 0;0 0 1] as for (b) and (c) i have no idea how to work them out...

Why stereographic projection preserves angles between curves but does not preserve area?

Alright so I am trying to find the projection matrix for the subspace spanned by the vectors [1] and [2] [-1] [0] [1] [1] I actually have the solution to the problem, it is ... P = [ 5 1 2 ] (1/6) [1 5 -2]...

Homework Statement How would i go about solving Proju(Proju(v))=Proju(v) Just a note Proju(v) means the projection of v onto you Homework Equations The Attempt at a Solution how would i go about solving this is mathematical terms, it is obvious when you do it...

Homework Statement A firefighting crew uses a water cannon that shoots water at 25.0 m/s at a fixed angle of 53.0 degrees above the horizontal. The firefighters want to direct the water at a blaze that is 10.0 m above ground level. How far from the building should they position their...

Figures that the only problem I have trouble with is the one the book considers to be "easy": 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...

Homework Statement After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 220 mph in the horizontal direction. If the package is to land right on the island...

Many books on QM state this so called von Naumann projection postulate i.e. that after the measurement system is in eigenstate of operator whose eigenvalue is measured. But in Landau Quantum Mechanics in chapter 7, author explicitly says that after the measurement system is in a state that...

hello again, I'm once again stumped, i was asked to find the rank and nullity of the projection u onto v so here is the given: T(u)=ProjvU, where v = <2,4> and this is what i did: let u = <u1 , u2> and plugged everything in the projection formula and ended up with < 4 + 2(u1) , -16 +...

Homework Statement Use the scalar projection to show that a distance from a point P(x1, y1) to the line ax + by + c = 0 is \frac{ax1 + by1 + c}{\sqrt{a^2 + b^2}}Homework Equations scalar projection = \frac{a . b}{|a|} The Attempt at a Solution The first thing that I did was to say that b =...

Homework Statement Hello! :smile: Find the equation of the projection of the line \frac{x}{4}=\frac{y-4}{3}=\frac{z+1}{-2} of the plane x-y+3z+8=0. So the line projects itself on the plane... Homework Equations The Attempt at a Solution First I find equation of line which...

Homework Statement The projection of the vector V onto (a,b) = (a,b) The projection of the vector V onto (-b,a) = (-b,a) Describe V in terms of a and b Homework Equations The Attempt at a Solution I let V=(x,y) then place that into the projection equation for each to get...