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hilbert-spaces

Solve Hilbert space problems using symbolic computation and theorem proving.

8|1|Updated Jan 4, 2026
Search Tags:#mathematics#functional analysis#hilbert spaces#orthogonal decomposition#projection theorem#riesz representation
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill hilbert-spaces
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: hilbert-spaces
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/functional-analysis/hilbert-spaces
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill hilbert-spaces

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to Hilbert spaces in functional analysis, simplifying complex mathematical operations.

Core Features & Use Cases

  • Orthogonal Decomposition: Decompose vectors in Hilbert spaces with respect to closed subspaces.
  • Projection Theorem: Prove the existence and uniqueness of nearest points in closed convex sets.
  • Riesz Representation Theorem: Demonstrate the equivalence between bounded linear functionals and inner product forms.
  • Parseval's Identity & Bessel's Inequality: Apply these fundamental identities for orthonormal bases.
  • Use Case: When analyzing signal processing algorithms that rely on Fourier series, this skill can help verify the properties of the basis functions and the representation of signals.

Quick Start

Use the hilbert-spaces skill to simplify the inner product expression <x + y, z>.

Frequently Asked Questions about hilbert-spaces

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I compute orthogonal decomposition of vectors in Hilbert spaces?▼

Orthogonal decomposition separates vectors into components relative to closed subspaces. This skill uses sympy to decompose vectors and compute their orthogonal projections symbolically.

Can I prove the Riesz representation theorem using symbolic computation?▼

Yes, the Riesz representation theorem can be demonstrated by showing the equivalence between bounded linear functionals and inner product forms. This skill uses sympy and z3 for symbolic operations and automated theorem proving.

What is the best way to verify Parseval's identity and Bessel's inequality for orthonormal bases?▼

Verifying Parseval's identity and Bessel's inequality involves applying fundamental identities to orthonormal bases. This skill provides computational tools to check these inequalities using symbolic mathematics.

Does this functional analysis tool require z3 and sympy to run?▼

Yes, this functional analysis tool requires both sympy and z3 dependencies. Sympy handles symbolic mathematical operations like inner product simplification, while z3 performs the automated theorem proving tasks.

How do I simplify inner product expressions like <x + y, z> in functional analysis?▼

Simplifying inner product expressions like <x + y, z> requires expanding the linear combination using inner product properties. This skill automates that algebraic expansion and simplification process using sympy.

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