Projections Definition and 97 Threads

Homework Statement If a=<3,-1> , find vector b such that comp_ab=2 Homework Equations comp_ab=\frac{a.b}{|a|} The Attempt at a Solution Still not entirely surecomp_ab is, exactly... is it C in the below? Lost...

I was reading the Scientific American latest edition and it was claimed that everything within the boundary of a particular timeframe volume can be described equally well by the projection of each event onto the surface. Is this accepted dogma? Suppose I picture (apparently I can't but...

This is a multifaceted question that pertains to both the academic and career fields, but since it has a little mode to do with academia, I thought posting here would be appropriate. I am soon to begin university, and I have recently developed a strong desire to get into physics research. I...

How did they do just before the crash of the 2000 tech bubble, for example? I've tried google, and it fails to produce anything relevant for the last 20 years

In cartesian coordinates (x.y,z) on the and (X,Y) on the plane, the projection and its inverse are given by the following formulae: (X,Y)=(x/1-z,y/1-z) (x,y,z)=(2X/1+X^2+Y^2, 2Y/1+X^2+Y^2, -1+X^2+Y^2/1+X^2 +Y^2) This relates to the field of differntial geo.Anybody have a proof to where thes...

Homework Statement Let T: R^2 -> R^2. Part a: Find a formula for T(a,b) where T represents the projection on the y-axis along the x-axis. Part b: Find a formula for T(a,b) where T represents the projection on the y-axis along the line L={(s,s):s is an element of R} Homework...

Homework Statement I have a force in three dimensions such that: F=600N Alpha(angle with x axis) = 120 Beta(angle with y axis) = 60 Omega(angle with z axis) = 45 I'm to find the projection of F along the y axis. The Attempt at a Solution I found the force vector for this force by...

Hi all, this is my first post, so forgive me if this is in the wrong forum. (I believe it does belong here) We are currently doing moments in physics and I have seen this in a few homework problems but can't seem to grasp it. For example, in one question, we are given a new axis AA that...

Homework Statement In three dimensions, consider the vector V = a1i + a2j +a3k. Determine the projections of V onto the x, y, z axis. Homework Equations These are formulas from my textbook related to projection: All underscores mean subscript. Proj_A B = (B * A/|A|) A/|A| = ((B * A)/(A * A))...

I am currently trying to understand the idea of quantum entanglement (more specifically the Bell inequality). But its brought up a lack of my knowledge of spin. So, I am trying to figure out how spin can be projected onto an arbitrary axis. Suppose there are two entangled electrons of...

Homework Statement Find the orthogonal projection of the given vector on the given subspace W of the inner product space V? V=R3, u = (2,1,3), and W = {(x,y,z): x + 3y - 2z = 0} I don't understand how to find the orthonormal basis for W? Homework Equations I don't understand how to...

Homework Statement I am part way done with this problem... I don't know how to solve part e or part f. Any help or clues would be greatly appreciated. I have been trying to figure this out for a couple days now. W={<x,y,z>, x+y+z=0} is a plane and T is the orthogonal projection on it. a)...

Do you have any idea of the algorithm used to make the projections for which candidate wins an election? How are tv stations able to do it with less than 5% of the vote?

Hi there...I need ur help on these questions: 1) Can H2O exist as a vapor at -40oc,As a liquid? Why? 2) What would be the general nature of Constant volume lines on Phase (P-T) diagram? Both questions are from Engg. Thermodynamics-Moran,Shaprio(Things engg. think abt section) Also, does anyone...

Homework Statement Find the projection of P in the direction of Q and the component of P orthogonal to Q. P=i-3j+k Q=-i+2j+5k Homework Equations ProjQ(P)={(P*Q)/(Q*Q)}Q OrthQ(P)=P-ProjQ(P)The Attempt at a Solution First I get P=(1,-3,1) and Q=(-1,2,5) ProjQ(P) =(-2/30)*(-1,2,5)...

I won't post the actual problem with numbers, I just need some direction. My teacher never went over this part of the webwork in class, and we haven't touched on it in physics either. "a" and "b" are both 3D vectors. 1.) I am supposed to find the component of "b" along "a" 2.) I am...

Hi! Studying the introductory chapters of a Operator Theory book, I have found that the author seem to find a lot of demonstrations "easy" and not worthy of demonstrations. Yet, I don't have such ease as he has... For instance, one that has bugged me (on several books) is the proof that...

Homework Statement Let P1 and P2 be the projections defined on R^3 by: P1(x1, x2, x3) = (1/2(x1+x3), x2, 1/2(x1+x3)) P2(x1, x2, x3) = (1/2(x1-x3), 0, 1/2(-x1+x3)) a) Let T = 5P1 - 2P2 and determine if T is diagonalizable. b) State the eigenvalues and associated eigenvectors of T...

Homework Statement Hi all - I've been battering away at this for an hour or so, and was hoping someone else could lend a hand! Q: Show that any Mobius transformation T not equal to 1 on \mathbb{C}_{\infinity} has 1 or 2 fixed points. (Done) Show that the Mobius transformation corresponding...

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How would you approach a question where you're given a curve in terms of a scalar equation, and asked to find the orthogonal projection of this curve in the yz-plane You know that the curve is the intersection of the surfaces of: x=y^2+z^2 --1 x-2y+4z=0 --2 From here, I would just...

Homework Statement Let P be a projection. The definition used is P is a projection if P = PP. Show that ||P|| >=1 with equality if and only if P is orthogonal. Let ||.|| be the 2-normHomework Equations P = PP. P is orthogonal if and only if P =P*The Attempt at a Solution I've proved the...

Homework Statement P is mxm complex matrix, nonzero, and a projector (P^2=P). Show 2-norm ||P|| >= 1 with equality if and only if P is an orthogonal projector (P=P*) Homework Equations Let ||.|| be the 2-norm The Attempt at a Solution a. show ||P|| >= 1 let v be in the range...

Homework Statement Suppose T ∈ L(V) and U is a subspace of V. Prove that U is invariant under T if and only if PUTPU = TPU.Homework Equations The Attempt at a Solution Consider u\inU. Now let U be invariant under T. Now let PU project v to U so that PU(v)=u. Therefore TPU(v)=T(u). Now since...

Say we have a transformation T\inL(V). Now suppose a subspace of V (U) is in the rangespace of T. Now suppose PUv=u with u=a1u1+...+amvm. Now apply T to u to get T(u)=b1u1+...+bmum=/=a1u1+...+amvm. What would happen if we apply PUto T(u)? In other words, what would we end up with after...

Aren't all projections orthogonal projections? What I mean is that let's say there is a vector in 3d space and it gets projected to 2d space. So [1 2 3]--->[1 2 0] Within the null space is [0 0 3], which is perpendicular to every vector in the x-y plane, not to mention the inner product of...

If V has finite dimension n, show that two projections have the same diagonal form if and only if their kernels have the same dimension. (A projection is defined to be a linear transformation P:V-->V for which P^2=P; V is a vector space). For the forward direction, I was thinking that if T...

Homework Statement The vector u of length 6 makes an angle of 40 with the z axis; it's vector projection on the xy plane makes an angle of 44 degrees with the x axis. The vector projection of a second vector v on the z axis has a length 5. The vector projection of v on the xy plane has a...

I'm re-visiting calculus again, and I've stumbled onto the concepts of scalar and vector projections in the vector chapter. While keeping in mind which equation to use for what projection is quite doable, I cannot seem to see the purpose of keeping scalar and vector projections in mind. Can...

OK, this question has a lot of parts, so I'll do my best to write it in a way that makes sense. Basically, aVR, AVL, and aVF are the three main vectors in the direction of blood being pumped by the heart. The three endpoints of the vectors form an equilateral triangle that goes from each hand...

Homework Statement Let R={[x,y,z,w]:x=y and z=w} and N={[x,y,z,w]:x=-y and z=-w} Find the rule in standard coordinates for the projection of R4x1 onto R along NHomework Equations The Attempt at a Solution I have B wrt R as {[1,1,0,0],[0,0,1,1]} and B wrt N as {[1,-1,0,0], [0,0,1,-1]}, so my...

Homework Statement Prove that if P in L(V) is such that P2 = P and every vector in Ker(P) is orthogonal to every vector in Im(P), then P is an orthogonal Projection. Homework Equations Orthogonal projections have the following properties: 1) Im(P) = U 2) Ker(P) = Uperp 3) v - P(v)...

[SOLVED] What are projections for? When do we need to use them? I understand the concept of projections, and I can do problems that require it pretty easily. But I don't get what the applications of projections are? Can anyone tell me some.

I was wondering if it is possible, in projections, to have a projected onto b equal to zero or undefined. In other words, when does a projected onto b equal zero and when is it undefined?

I am not sure if I am posting this in the right forum or not. I had impression that there is just no difference between projection of a vector and its components until I took the Statics course. We are following The Engineering Mechanics : Statics book by Meriam and Krage. I got stuck up in...

Let \overrightarrow v and \overrightarrow w be vectors in R3. Prove that \overrightarrow w - {\rm{proj}}_{\overrightarrow v } \overrightarrow w is perpendicular to \overrightarrow v . Here's my attempt: \begin{array}{l} \left( {\overrightarrow w - {\rm{proj}}_{\overrightarrow v }...

[SOLVED] Projections on subspaces Homework Statement I have some questions on this topic: 1) If I have an orthonormal basis for a subspace U and I have a vector A, and I want to find the orthogonal projection of A onto U, then I use the expression written here...

Homework Statement Consider the following two vectors v1= (cosx , sinx)(transpose) , v2= (-sinx , cosx)(transpose). Compute the projectors P1, P2 onto the vectors v1 and v2. Homework Equations (a1) (a1*,b1*) (A) <---input (b1) ...(B) This is a matrix that projects on column...

I've now encountered two different definitions for a projection. Let X be a Banach space. An operator P on it is a projection if P^2=P. Let H be a Hilbert space. An operator P on it is a projection if P^2=P and if P is self-adjoint. But the Hilbert space is also a Banach space, and there's...

Given: \vec A \cdot \vec B = non zero and \theta does not equal 0 I can't seem to prove that Vector B minus the Projection of B onto A makes the orthogonal projection of B onto A. Can you help?

Hello, Can anyone tell me what the triangles, squares, and ovals mean in the projection on page 19? Does this have something to do with the directions for the third axis? On the next page several of the symbols are black. What significance does this have, also? Thanks -scott "[PLAIN...

Homework Statement Consider a symmetric n x n matrix A with A² = A. Is the linear transformation T(x) = Ax necessarily the orthogonal projection onto a subspace IR^n? Homework Equations The Attempt at a Solution No idea what thought to begin with.

Hi guys, Could anyone give me any information on Gutzwiller Projections? What exactly is it, and why is it needed? I guess i am saying, what does it mean to Gutzwiller project a wavefunction, and how do you go about such a process? I have searched around but i have been getting bogged down...

As a projectile moves along its parabolic trajectory, which of the following remain constant (ignoring air resistance, and defining the z-axis to point upward)? More than one answer may be correct! a. Its speed. b. Its velocity. c. Its x-velocity and its y-velocity. d...

Is there ANY scientific basis of OBEs or Astral Projections, or remote viewing?:confused: and whether it is possible or not to project astrally?

Would it be possible to use holographic projections to make you look like something else? I mean, for example, could you project an image onto your body (With like a hand-held projector) to make you look like a different thing?

Ok, I'm working with the Pauli Matrices, and I've already gone through showing a few bits of information. I've got a good idea how to keep going, but I'm not exactly sure about this one-- say M= 1/2(alphaI + a*sigma) where alpha E C, a=(ax, ay, az) a complex vector, a*sigma=ax sigmax+ay...