Projection Definition and 434 Threads

This is from my Vector Analysis course today. We've been doing a bit of abstract stuff since class began, but the professor said we're going to get to concrete stuff pretty quickly. I think the notation is throwing me off a bit. I'm not sure why the alphas change for each successive...

on U, where U = span{(1, -1, 1, -1), (2, 0, -3, 1)}

This problem refers specifically to http://books.google.com/books?id=W9ZuLZWldUoC&lpg=PA9&ots=2lrfqlB3j7&dq=%22stress%20components%20on%20an%20arbitrary%20plane%22&pg=PA10#v=onepage&q=%22stress%20components%20on%20an%20arbitrary%20plane%22&f=false". The text comments that Area BOC =...

Sorry 'bout posting so many topics but there are too many things that are unclear to me. CMBR measurements suggest the universe is pretty much FLAT, but I don't see it as flat, and forget our planet, all those vast spaces in every spatial dimension - all that is flat? It obviously has depth...

Hello everyone, If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of (x-y)’, denoted as row( (x-y)’...

Homework Statement Well, I was trying to find an equation that would let me calculate what angle I have to put my gun at to get the projectile to hit a specified distance. Not actual homework, but something I'm trying to do for a game (Garry's mod) So the initial velocity of the shell...

I was reading Lie Algebras in Physics by Georgi......second edition... Theorem 1.2: He proves that every finite group is completely reducible. He takes PD(g)P=D(g)P ..takes adjoint...and gets.. P{D(g)}{\dagger} P=P {D(g)}{\dagger} So..does this mean that the projection...

edit: This thread might need moved, sorry about that. Hi, I have ended up on this site a few times after searching various maths issues; it seems to have a good community so I am asking you good people for a little help understanding this. Tomorrow I have a semi-important maths exam, if I fail...

[b] Def1. Let L be a line in E. We define the "orthogonal projection onto L" to be Ol = {(P,Q)| P,Q in E and either 1.P lies on L and P=Q or 2.Q is the foot of the perpendicular to L through P. Problem 1. Let L be a line in E. Show that Ol is not a rigid motion because it fails...

Let A be a matrix corresponding to projection in 2 dimensions onto the line generated by a vector v. A) lambda = −1 is an eigenvalue for A B) The vector v is an eigenvector for A corresponding to the eigenvalue lambda = −1. C) lambda = 0 is an eigenvalue for A D) Any vector w perpendicular to...

I was reading about a certain methood that uses projection to calculate the probability of finding a particle in a certain state. The explanation is not detailed enough for me to get my head around how to use it, but maybe some of you people are familiar with the methood? The methood goes like...

Homework Statement A ball was projected at an angle A to the horizontal. One second later another ball was projected from the same point at an angle B to the horizontal. One second after the second ball was released, the two balls collided. Find the speed of projection for the two balls...

Homework Statement Determine the matrix for the spatial projection perpendicular to the straight line (x1, x2, x3) = t(1, 2, 3). The vector space is orthonormal. Homework Equations The Attempt at a Solution After a trip to #math on freenode that resulted in discussions of Gram-Schmidt...

Quantum - Projection Probability - "Projection amplitudes for SHO states." Given the two normalized 2D SHO wave functions <x,y|mx[/SUB ],ny> for the second energy level n = nx + ny = 1 in the m[SUB]x[/SUB ],n[SUB]y representation: <x,y|1,0> = (2/pi)1/2xexp[-(x2+y2)/2] <x,y|0,1> =...

Homework Statement Give an example of a subspace W of a vector space V such that there are two projections on W along two distinct subspaces. Homework Equations The Attempt at a Solution I tried looking into Euclidean geometry spaces (R3 and R2) but no matter what subspace W I...

Homework Statement curve S is the intersections of two surfaces, i have to find the curve obtained as the orthogonal projection of the curve S in the yz-planeHomework Equations how do i find the orthogonal projection of curve S??The Attempt at a Solution i found the equation of curve S to be...

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...

Homework Statement Find a projection [matrix] E which projects R2 onto the subspace spanned by (1,-1) along the subspace spanned by (1,2).Homework Equations P = \frac{a a^{T}}{a^{T} a}The Attempt at a Solution Computing P... P = \[ \left( \begin{array}{ccc} \frac{1}{2} & -\frac{1}{2}\\...

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...

Homework Statement Show that if A is a normal operator in an n-dimensional vector space, and if A has r distinct eigenvalues a1,a2,...ar, then the projection operator onto the subspace with eigenvalue ai can be written as: Pi=[(A-a1)...(A-aa-1)...(A-ar)]/[(ai-a1)...

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...