Suppose I want to Project the function $f(x,y)$ onto the function $g(x,y)$ (both defined on $R_+$). Can it be done by it be done by the following: $$Proj_f \rightarrow g = \frac{<f,g>}{<g,g>} \times g $$ , where $<f,g> = \int \int_{R_+} f.g dx dy$
2026-03-27 03:48:19.1774583299
Multivariate Orthogonal Projections:
62 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Proving the differentiability of the following function of two variables
- If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Number of roots of the e
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- How to prove $\frac 10 \notin \mathbb R $
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
Related Questions in FUNCTIONAL-ANALYSIS
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- Prove or disprove the following inequality
- Unbounded linear operator, projection from graph not open
- $\| (I-T)^{-1}|_{\ker(I-T)^\perp} \| \geq 1$ for all compact operator $T$ in an infinite dimensional Hilbert space
- Elementary question on continuity and locally square integrability of a function
- Bijection between $\Delta(A)$ and $\mathrm{Max}(A)$
- Exercise 1.105 of Megginson's "An Introduction to Banach Space Theory"
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
Related Questions in ORTHOGONALITY
- Functions on $\mathbb{R}^n$ commuting with orthogonal transformations
- Proving set of orthogonal vectors is linearly indpendent
- Find all vectors $v = (x,y,z)$ orthogonal to both $u_1$ and $u_2$.
- Calculus III Vector distance problem.
- Is there a matrix which is not orthogonal but only has A transpose A equal to identity?
- Number of Orthogonal vectors
- Find the dimension of a subspace and the orthogonality complement of another
- Forming an orthonormal basis with these independent vectors
- orthogonal complement - incorrect Brézis definition
- Orthogonal Projection in Inner Product
Related Questions in PROJECTIVE-SPACE
- Visualization of Projective Space
- Poincarè duals in complex projective space and homotopy
- Hyperplane line bundle really defined by some hyperplane
- Hausdorff Distance Between Projective Varieties
- Understanding line bundles on $\mathbb{P}_k^1$ using transition functions
- Definitions of real projective spaces
- Doubts about computation of the homology of $\Bbb RP^2$ in Vick's *Homology Theory*
- Very ample line bundle on a projective curve
- Realize the locus of homogeneous polynomials of degree $d$ as a projective variety.
- If some four of given five distinct points in projective plane are collinear , then there are more than one conic passing through the five points
Related Questions in PROJECTION
- What's wrong with my reasoning regarding projections
- Finding the orthogonal projection of a vector on a subspace spanned by non-orthogonal vectors.
- Coordinates of camera bounding box projected on another object.
- Bounded projection
- Deriving principal component out of cosine similarity
- Projection onto the space spanned by eigenfunctions in a Hilbert space
- Show that T - I is a projection.
- Pose estimation from 2 points and known z-axis.
- Non orthogonal projection of a point onto a plane
- Mercator projection - Use existing equation to solve for degrees
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?