Questions tagged [projection]

Question 1

Two circles are drawn on a sphere, having a single common point. Prove that the center of the sphere, the centers of both circles, and their common point lie in the same plane. This is equivalent to :...

Question 2

Let's say it's 200 B.C. and you're tasked with building all of modern math from the ground up. Let's say also that we already intuitively understand the concepts of a "vector", the "...

Question 3

Let $X$ a manfiold and $\Delta=\{(x,x), x \in X\}$ the diagonal of $X \times X$. Denote by $E$ the normal vector bundle of $\Delta$ and $TX$ the tangent bundle of $X$. Denote by $\pi: E \rightarrow \...

Question 4

Let $\mathcal{H}$ and $\mathcal{K}$ be a real Hilbert space, $U\subseteq \mathcal{H}$ a closed linear subspace and $T\in\mathcal{B}(\mathcal{H},\mathcal{K})$ a continuous linear operator. I am ...

Question 5

On a plane, give a line $d$ and the vectors $\overrightarrow{u}, \overrightarrow{v}\ne\overrightarrow{0}$ such that $\overrightarrow{u},\overrightarrow{v}$ are not perpendicular to the line $d$. Let $...

Question 6

Consider $P$ to be the union of polygons inside a $3\rm{D}$ space. Find the minimal possible area of $P$ provided that the projection of $P$ onto the axis planes is a unit square. This is a question ...

Question 7

Let $X$ be a Hilbert space and $T: X \to X$ be a continuous linear operator with ${\rm dim}({\rm ker} T)=n<\infty $. Moreover, let $P$ and $P^{\perp}$ denote the orthogonal projections onto ${\rm ...

Question 8

Let $K = \mathbb{R}$ or $\mathbb{C}$ and $n \in \mathbb{N}, n \geqslant 2$. I was thinking about the topology of two subsets of $\mathfrak{M}_n(K)$ we don't talk about very often in Matrix Topology ...

Question 9

Is there a (bounded) solid other than the sphere so that its orthogonal projection on any plane is always the same? By "the same" I mean every projection is congruent to each other. I ...

Question 10

I'm working on an $n$-dimensional sphere $S^n ⊂ \mathbb R^{n+1}$ and need to restrict a symmetric matrix S to act only within the tangent space of the sphere. I've encountered the expression: $$E^T S ...

Question 11

What would be a projection of a finite right cone with base radius $R$ and height $H$ which is tilted about an angle $\theta$ with the vertical on a vertical. I have an intuition that it may look ...

Question 12

I am following the book "The $P(\Phi)_2$ Euclidean (Quantum) Field Theory" by Simon. I will rephrase the result to make it general and not require any context on quantum field theory. Let $A,...

Question 13

Let $X$ be a Banach space and $P:X^* \to X^*$ a (bounded linear) projection, i.e., $P^2 = P$. I would like to know whether the following statement is true: Claim. If $\operatorname{Im}(P)$ is $\sigma(...

Question 14

Let $X$ be an infinite-dimensional Banach space and $Y$ a finite-dimensional Banach space. It is a standard fact that if $T: X \to Y$ is a linear operator and $\ker(T)$ is norm-closed, then $T$ is ...

Question 15

According to MathWorld's "Cork Plug" entry a cork plug is a shape that can stopper a circular, triangular, or square hole. Could you create a plug that could stopper a circular, triangular, ...

Stack Exchange Network

Questions tagged [projection]

Prove that the center of the sphere, the centers of two small circles, and their single common point lie in the same plane

Is there an intuitive way to understand this formula for the magnitude of the projection of one vector onto another? [duplicate]

Diagonal and Normal Bundle Isomorphism on a Manifold [closed]

Is this true in Hilbert spaces? $P_{T(U)}=TP_UT^+$

Show that $pr_d(\overrightarrow{u}+\overrightarrow{v}) = pr_d\overrightarrow{u} + pr_d\overrightarrow{v}$

Minimal possible area of a given union of polygons.

Whether the restriction of a continuous linear operator with finite dimensional kernel to the orthogonal complement of the kernel is an isomorphism?

Topology of projection matrices and symmetry matrices

A solid that looks the same from every angle

Why does $E^T S E$ restrict a symmetric matrix $S$ to the tangent space? Looking for references.

Projection of cone

How is the Markov property about projections non-trivial?

If $P:X^* \to X^$ is a projection with weak$^$-closed range, is $P$ weak$^*$-continuous?

If the kernel of an operator is $\omega^$-closed, is the operator $\omega^$-continuous?

Generalizing the Cork Plug

Hot Network Questions