I am researching multivariate medians. In one of my sources it is stated that "Liu showed that the simplicial median is invariant to affine transformations". I am a bit confused about what this means. I know that affine transformations preserve ratios of distances, collinearity but not necessarily angles or lengths. However, I don't know what it means for something to be invariant to affine transformations. Does it mean that it will always remain the same? Also I was wondering if there is a simple example to illustrate this to help improve my understanding.
2026-02-22 17:51:54.1771782714
What does invariant to affine transformations mean?
6.4k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in AFFINE-GEOMETRY
- Prove that Newton's Method is invariant under invertible linear transformations
- Equality of affine subsets
- How do you prove that an image preserving barycentric coordinates w.r.t two triangles is an affine transformation?
- Show that $\mathcal{I}(V)$ is the product ideal of $k=\mathbb{F}_2$
- Affine Spaces Exersice
- Intersection of two affine subspaces in vector space
- Averages of side and averages of angles in a triangle
- Prove that a Balanced Incomplete Block Design with parameters $(n^2, n^2+n, n+1, n, 1)$ is a finite Affine Plane
- Proving an affine transformation preserves distance.
- Connectedness and path connectedness, of irreducible affine algebraic set in $\mathbb C^n$, under usual Euclidean topology
Related Questions in MEDIAN
- Is the median a function?
- Expected value of a sample median from a sample of size $\sqrt{n}$ taken from a set of $n$ numbers
- Median estimated from grouped data with a single class
- Medians from paired data
- Let $X_1$, $X_2$, $X_3$ be i.i.d. continuous random variables from Exponential Distribution.
- how to derive median from conditional median?
- Median of obtuse triangle
- Median value of a function
- Non-Existence of the Cumulative Distribution Function of a Discrete Random Variable at Median
- Difference in the concept of medians
Related Questions in INVARIANCE
- A new type of curvature multivector for surfaces?
- Is a conformal transformation also a general coordinate transformation?
- What does invariant to affine transformations mean?
- Matrix permutation-similarity invariants
- system delay: $x(2t-t_o) \,\,or \,\, x(2t-2t_o)$?
- Writing a short but rigorous proof
- Poles and Zeros of a Linear Transform
- Two Player Strategy Game
- Rigorous proof to show that the $15$-Puzzle problem is unsolvable
- Projective invariants of quadrilaterals/group of quadrilaterals
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?
Affine transformation are a combination of a translation with a linear transformation
$$A(v)=Av+v_0$$
which preserves points, straight lines and planes.
Ratio by segments are preserved and in particular mean points are preserved by linearity
indeed if $$M=\frac{P+Q}{2}\implies A(M)=\frac{A(P)+A(Q)}{2}+v_0$$
Affine transformations