Projection Definition and 409 Threads

Can you tell if the ring will be beta or alpha in the haworth projection, chair conformation by just looking at the Fischer projection, or must you be told first before creating the two from the Fischer? If so, could someone explain how? I've seen a bunch of websites and they all seem to say...

Let's say i have 2 arbitrary vectors in a 3d space. I want to project Vector A to Vector B using a specified normal. edit: better image A is green, B is red, C is red arrow. Blue is result. In this case, i want to project green vector to red vector in the red direction. This would give me...

Suppose a plane contains the origin and has normal $n$. Is it true that the projection of a vector $u$ on the plane along vector $v$ is $(v\times u)\times n$, where $\times$ denotes the cross product? I can see that the direction is right, but I am not sure about the length. Links to textbooks...

If we express the projection operator with vectors, we get ##\hat{P}\vec{v} = \vec{e}(\vec{e}\vec{v})## which means that we project ##\vec{v}## onto ##\vec{e}##. We can write this as ##\hat{P}\vec{v} = e_k \sum_{l} e_lv_l = \sum_l (e_ke_l )v_l##. In my class we said that the matrix for the...

Homework Statement Let ##V = \mathbb{R}^4##. Consider the following subspaces: ##V_1 = \{(x,y,z,t)\ : x = y = z\}, V_2=[(2,1,1,1)], V_3 =[(2,2,1,1)]## And let ##V = M_n(\mathbb{k})##. Consider the following subspaces: ##V_1 = \{(a_{ij}) \in V : a_{ij} = 0,\forall i < j\}## ##V_2 =...

Homework Statement x = <0, 10, 0> v1 = <4, 3, 0> v2 = <0, 0, 1> Project x onto plane spanned by v1 and v2 Homework Equations Projection equation The Attempt at a Solution I took the cross product k = v1xv2 = <3, -4, 0> I projected x onto v1xv2 [(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p I finished...

Hello! (Wave) Let $W$ be the subspace of $\mathbb{R}^3$ that is orthogonal to the vector $w_1=(-1,-1,1)$ and $p=(x,y,z)$ the projection of the vector $v=(-1,1,2)$ onto $W$. What is $7x-11y+5z$ equal to?I have thought the following: $\text{proj}_Wv=\frac{\langle v, w_1\rangle}{\langle w_1...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution The solution is obviously given, but I don't really understand what is done there. What method is being used? so I can understand, because i see how they attained v, but then that vector normalised is not correct is it?

Take a projection operatorPm=|m><m| However if the ket of m is a column matrix of m x 1 and its bra the complex conjugate with 1 x m length therefore <m|m> = |m|2 since the m here is the same since projection operator is the same. if A is a matrix B = A A*B=B*A but Pm*Pm = Pm (Projection...

I once took notes from a website, and now I cannot find the reference anymore, so I am attempting to reconstruct it, and am sure that I have it all wrong (or that the website did, or both). Hence, I would be grateful for corrections. My apologies for not being able to provide the link. The...

I have a very very unusual project requirement where I need a pocket video projection with the lowest possible projection angle or "longest possible throw-ratio". It's a pocket DLP projector so goal is to have the beam remain ,as much as possible, almost the same size as the DLP matrix, for a...

A bit of unsual scenario, I need to divide a video projection beam horizontally into two. Since the splitted beams in my diagram are treated as a separate beam they have to have their focus plane changed. Is that possible to do and how would one do it? http://image.ibb.co/jAu9x7/9241421.jpg If...

Homework Statement Given two vectors u→=(16,5,2) and v→=(3,−2,−2) find the following: The coordinates of the projection of u→ on v→The magnitude of the projection of u→ on v→ . Homework EquationsThe Attempt at a Solution I have never done a question like this before, I was curious did I do...

The Wikipedia article Quantum Indeterminacy discusses the measurement problem and possible reasons why measurement values are inherently random. In the section labeled "Measurement", the Projection Postulate is briefly discussed. After explaining the Projection Postulate, in the second...

Homework Statement Obtain a 4×4 projection matrix that maps ##ℝ^3## to the plane 3x + 2y = 1. Assume that the centre of projection i.e. eye is at (0,0,0). The problem that my problem is strongly based on and its solution are #3, here. (I'm referring to the first way of solving the problem in...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.5.3 ... Duistermaat and Kolk"s Example 1.5.3 reads as follows:In the above example we read the...

Homework Statement Derive the relativistic Euler equation by contracting the conservation law $$\partial _\mu {T^{\mu \nu}} =0$$ with the projection tensor $${P^{\sigma}}_\nu = {\delta^{\sigma}}_\nu + U^{\sigma} U_{\nu}$$ for a perfect fluid. Homework Equations $$\partial _\mu {T^{\mu \nu}} =...

Homework Statement Being F = (1,1,-1), the orthogonal projection of (2,4,1) over the orthogonal subspace of F is: a) (1,2,3) b) (1/3, 7/3, 8/3) c) (1/3, 2/3, 8/3) d) (0,0,0) e) (1,1,1) The correct answer is B Homework Equations The Attempt at a Solution Using the orthogonal projection...

Homework Statement A water balloon is fired 34 m/s from a water cannon, which is aimed at an angle of 18° above the ground. The centre of the cannon's target (which has a radius of 1.0m) is painted on the asphalt 42m away from the water cannon. a) Will the balloon hit the target? Justify your...

Hello, I want to show $ T^{*}(Pr_{C}(y)) = Pr_{T^{*}(C)}(T^{*}y)$ where $T \in B(H)$ and $TT^{*}=I$ , $H$ is Hilbert space and $C$ is a closed convex non empty set. but i don't know how to start, or what tricks needed to solve this type of problems. also i want know how to construct $T$ to...

Hello, my book shows this figure of Fischer formula of D-glucose I don't understand this figure, and I wonder why the upper carbon atoms in both the right and left formulas have 5 bonds. And from where comes this hedrogen atom in the upper left side of the figure (attached to alpha...

I haven't touched a physics textbook in a while and need help with something fairly simple. I am staring straight down on a rectangular prism that is tilted on one axis to a known angle, theta. I have a measurement of a vector length in this orientation. I would like to know how much that length...

Hi, I can't seem to work out how angle of projection for maximum range comes out to be (pi/4 - Beta/2) This happens when the projectile is protected up the inclined plane. Similarly, I couldn't understand how the angle comes out to be (pi/4 + Beta/2) when the projectile is protected down the...

Well, this might be the stupidest question ever, but whatever. I was just thinking about a problem where a pendulum is attached to something that spins around itself (image below) and thought that maybe Centripetal Force might be a projection of tension on a vector that is perpendicular to ω...

Hello everyone. I have this problem: 1. The problem statement, all variables and given/known d I throw stone from height h at an angle α, then at an angle β (so I know h, α, β). I throw it with same velocity v. The stones fall in same distance d. The question is: find the d (distance) and v...

So the circle minus the pole is homeomorphic to the number line. Does that mean that the pole itself represents a number that doesn't exist on the real line? After all, the pole certainly exists and yet is the only point that isn't mapped.

Is the beam of a pulsar projected perpendicular to its spin? If so, is the "pulse" due to wobble?

Lets assume we are mapping one face of earth. we place a plane touching the Earth at 0 lattitude and 0 longitude. Now we take the plane of projection. suppose that we expand the projection unevenly. The small projectional area of a certain lattitude and longitude is expanded by a factor which is...

In two papers of Terrel and Penrose, the concept of Terrel effect were presented. Both of the papers say that "the plane of projection is expanded by a certain factor, which is equal to Doppler factor for certain cases." Now does it mean the area of the projected plane is expanded by that...

Two questions regarding the completeness relation: First: I understand that the completeness relation holds for basis vectors such that ## \sum_{j=1}^{m} | n_{j} \rangle \langle n_{j} | =\mathbb{I}##. Does it also hold for unit-normalized sets of state vectors as well, where ## | \phi_{j}...

Homework Statement What's the projection of the resultant force onto an said axis? Homework Equations Sine Law, Cosine Law The Attempt at a Solution For problem 2/20, the projection onto the b axis was found by multiplying the resultant force by the cosine of 30 degrees. Why does this method...

I am learning about shearing stress, and I am a little confused about the area of projection mentioned in my book. When it introduces it, it shows a plate with a rivet through it. The plate is of thickness t, and the diameter of the rivet, d. It shows the plate and the rivet cut in half by a...

Homework Statement Draw the third view and the points on each view. In the first picture you have what the exercise has given us and in the second what I have drawn. I have turned the page so that the first view is the one on the left, the horizontal one is the one on the right. Is that OK...

I am looking for free solved exercises about: right angle projections, (cross) section views Here are some pictures of my book so you can understand what I am looking for http://1.1m.yt/3cNNDl-.jpg http://1.1m.yt/FekMn6x.jpg http://1.1m.yt/1t3KEer.jpg http://1.1m.yt/urA5V2_.jpg...

Homework Statement We have to make right angle projections of various objects. Are these projections correct?Homework EquationsThe Attempt at a Solution https://postimg.org/image/tg987f8bx/ https://postimg.org/image/rcyszr8j1/ https://postimg.org/image/64l4ibu25/...

I'm attempting to reclaim lost knowledge... hopefully this works. I would like to take a data set I have x,y values and project the trend beyond the (10) values I currently have. For example, I have a graph with (10) values for x and y, but would like to graph the trend created by values 1-10 to...

Does anyone know how I could convert data from Planck, which appear as an oval shape, into a form that I can easily map onto a sphere (ie. a rectangular shape in 2:1 aspect ratio)? Here is an example Planck image: http://sci.esa.int/science-e-media/img/61/Planck_CMB_Mollweide_4k.jpg I see that...

Homework Statement Let q ∈ C^m have 2-norm of q =1. Then P = qq∗ is a projection matrix. (a) The matrix P has a singular value decomposition with U = [q|Q⊥] for some appropriate matrix Q⊥. What are the singular values of P? (b) Find an SVD of the projection matrix I − P = I − qq∗ . In...

I know that to find the projection of an element in R^n on a subspace W, we need to have an orthogonal basis in W, and then applying the formula formula for projections. However, I don;t understand why we must have an orthogonal basis in W in order to calculate the projection of another vector...

Homework Statement Find the volume of solid which is bounded by z = 4-x-y and below by region in the plane of 0<x<2 , 0<y<1 When i use zx -plane projection , i found that my ans is different with the ans of using xy projection ...Which part i did wrongly ? From the ans given , volume = 5...

Homework Statement 2. and 3. Relevant equations and the attempt at a solution We find the L^2 projection as such: <b_j , e_j > , where e_j is orthonormal basis j. Now set b_j = < x^2 , e_j > for 1 \leq j \leq 3 .

To compute the vacuum expectation value ##\langle \Omega | T\{q(t_{1})\cdots q(t_{n})\}|\Omega\rangle## in the path integral formalism, we start with the time-ordered product in the path integral representation ##\langle q_{f},t_{f}|\ T\{q(t_{1})\cdots q(t_{n})\}\ |q_{i},t_{i}\rangle=\int\...

Homework Statement Determine the magnitude of the projection of force F = 700 N along the u axis Homework EquationsThe Attempt at a Solution A(-2, 4, 4) r(AO) = 2i -4j - 4k r(AO mag)= 6 u(AO) = 1/3i - 2/3j - 2/3k F(AO) = 233.3333i - 466.6667j - 466.6667k I'm not sure where to go from here...

What mathematical operation does this expression represent" |i><i| I know the i's are unit vectors, and I know <i|i> is the dot product, but what operation is the ket-bra?

Hi, Sorry this is an unusual thread and question, but I figured people here might be able to explain the physics of what is going on in this image I came across a few images of an underground music club in Berlin where an image of stained glass art you would find in a church is being projected...

Homework Statement One Second after vertical projection. a body is at the height of 10m and still moving upward. find it's initial speed and the height it will reach 1 second later. Compute the Maximum Height Homework Equations vf^2=vi^2+2ad The Attempt at a Solution Vf = 0 m/s Vi = ? Height =...

Hi everyone. I was working on a problem for days. The problem statement is: "Consider points P(2,1,3), Q(1,2,1), R(-1,-1,-2), S(1,-4,0). Find the shortest distance between lines PQ and RS." Now, I did the following formula: PS dot (PQ x RS) / magnitude of (PQ x RS). (For skew lines) Now...

I know that projection of vector B on A is ||B||cos(theta) where theta is the angle between vector A and B . But why do we find it . Is there any application for this

Homework Statement A projectile is fired with a velocity of 60 m per second at an angle, theta, from a horizontal ground towards the roof of a tunnel of height 5m. If the projectile just barely touches the roof, determine the a) angle of projection b) time of the flight c) range of the...

Hello everyone, I was playing around with some equations regarding air resistance. I tried to calculate the height that is reached by an object that is projected vertically into the air. However something seems to go wrong when integrating. Starting with the equation of motion \begin{align*}...