I am trying to derive the dual of weighted $L_1$ norm. Assume weights are all non-negative. Let $x \in R^2$
$$|| x ||_{1,w} = w_1 |x_1| + w_2 |x_2| $$
How do weights affect the dual norm?
2026-03-25 15:41:11.1774453271
Dual norm of Weighted L1
313 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DUALITY-THEOREMS
- Computing Pontryagin Duals
- How to obtain the dual problem?
- Optimization problem using Fenchel duality theorem
- Deriving the gradient of the Augmented Lagrangian dual
- how to prove that the dual of a matroid satisfies the exchange property?
- Write down the dual LP and show that $y$ is a feasible solution to the dual LP.
- $\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?
- Group structure on the dual group of a finite group
- Proving that a map between a normed space and its dual is well defined
- On the Hex/Nash connection game theorem
Related Questions in DUAL-SPACES
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- How to conclude that $\ell_\infty$ is not separable from this exercise?
- Dual of linear map into a tensor product
- Basis of vector spaces in perfect pairing
- How to find a dual basis given a basis?
- $T \in \mathcal L(V,W)$ is surjective $\iff ($range $T)^0 = \{0\}$
- Restrict $g$ to a dense subclass in $\|f\|_p=\text{sup}\{|\int_Xfg|:\|g\|_{p'}\leq 1\}$
- $(\text{Im}(T^*))^0 = \ker(T)$?
- Unit ball in dual space is weak*separable
- Co- and contravariance of vectors vs co- and contravariant functors
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?