Let $\mathcal{V}=\{\overrightarrow{AB}\;| A, B \in \mathbb{R}^2\}$. On $\mathcal{V} \backslash\{0\}$ define following equivalence relation: $v\sim w \iff \exists\lambda\in\mathbb{R}^{*}$ such that $v=\lambda w$.
How can I identify quotient set $\mathcal{V}\backslash\{0\}_{/\sim}$ as geometrically object?
2026-04-06 11:55:53.1775476553
How can I identify quotient set $\mathcal{V}\backslash\{0\}_{/\sim}$ as geometrically object?
21 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
Related Questions in EQUIVALENCE-RELATIONS
- Relations of equivalence...
- Number of subsets, relations etc of a set
- Number of possible equivalence relations
- Why is $p(z) = \frac{e^z}{1 + e^z} \color{red}{\equiv} \frac{1}{1 + e^{-z}}$ and not $=$?
- Simple question about relations
- Total number of equivalence class for a set
- Is this an equivalence relation and explaination?
- Partition of a set identified by a equivalence relation
- Define an equivalence relation on $\{ 1,2,3,4 \}^2$ by: (, )(, ) if ⋅ = ⋅ . How many equivalence classes are there?
- Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even
Related Questions in QUOTIENT-SPACES
- How to find the Fuschian group associated with a region of the complex plane
- Coset and Fiber
- Proof of Existence of Quotient Topology
- Quotient Spaces and Dimension
- Intersection of Quotient Spaces
- From $[0,1]\times [0,1]$ construct the Klein bottle
- Nice neighborhoods of each "piece" in a manifold connected sum
- A connected manifold $N$ can be identified with its universal covering quotient a discrete group
- How to find dimension of a given quotient vector space?
- Find the ideals of $S^{-1}R$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?