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vector-spaces

Solve vector space problems using SymPy and Z3 symbolic computation.

3.9k|296|Updated Dec 23, 2025
Search Tags:#vector spaces#linear algebra#subspace#linear independence#basis#change of basis
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill vector-spaces-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: vector-spaces
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/linear-algebra/vector-spaces
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill vector-spaces-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

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

What problem does it solve?

This Skill provides a structured approach and computational tools to solve common problems related to vector spaces in linear algebra, such as checking for subspaces, determining linear independence, finding bases, and performing change of basis.

Core Features & Use Cases

  • Subspace Verification: Checks if a set of vectors forms a subspace by verifying the presence of the zero vector and closure under addition and scalar multiplication.
  • Linear Independence: Determines if a set of vectors is linearly independent by analyzing the null space of the matrix formed by these vectors.
  • Basis and Dimension: Identifies a basis for a vector space and calculates its dimension by finding pivot columns after row reduction.
  • Change of Basis: Guides the process of finding a transition matrix to convert coordinates between different bases.
  • Use Case: When faced with a complex linear algebra problem involving vector spaces, this skill offers a step-by-step guide and automates calculations using symbolic math tools.

Quick Start

Use the vector-spaces skill to check if the set of vectors forms a subspace.

Frequently Asked Questions about vector-spaces

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

FAQPage Schema
How do I check if a set of vectors forms a subspace in linear algebra?▼

To verify a subspace, check for the presence of the zero vector and confirm closure under addition and scalar multiplication. This Skill automates subspace verification using symbolic computation to systematically validate these properties.

How do I determine if vectors are linearly independent using SymPy?▼

Determine linear independence by analyzing the null space of the matrix formed by the vectors. This Skill uses SymPy to construct the matrix and evaluate its null space to confirm linear independence.

What is the best way to find a basis and calculate the dimension of a vector space?▼

Find a basis and calculate dimension by identifying pivot columns after row reduction. This Skill automates basis identification and dimension calculation by performing symbolic row reduction operations.

How do I find a transition matrix for change of basis operations?▼

Find a transition matrix to convert coordinates between different bases. This Skill guides the change of basis process and automates the computation of transition matrices using symbolic math tools.

Can I use Z3 for theorem proving in linear algebra vector space problems?▼

Yes, you can use Z3 for theorem proving in linear algebra. This Skill leverages Z3 alongside SymPy to provide computational tools and systematic strategies for solving vector space problems.

Do I need Python and symbolic math libraries to solve vector space problems?▼

You need Python with SymPy and Z3 installed to solve vector space problems. This Skill relies on these dependencies for symbolic computation and theorem proving to automate calculations.

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