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eigenvalues

Compute eigenvalues and eigenvectors using SymPy and verify with Z3.

3.9k|296|Updated Dec 23, 2025
Search Tags:#mathematics#eigenvalues#linear algebra#sympy#eigenvectors#matrix computation
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill eigenvalues-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: eigenvalues
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/linear-algebra/eigenvalues
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill eigenvalues-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 to solving eigenvalue and eigenvector problems in linear algebra, automating complex calculations.

Core Features & Use Cases

  • Characteristic Polynomial Computation: Calculates the characteristic polynomial of a given matrix.
  • Eigenvalue Calculation: Solves the characteristic polynomial to find the eigenvalues.
  • Eigenvector Calculation: Determines the eigenvectors corresponding to each eigenvalue.
  • Verification: Uses symbolic math tools to verify the computed eigenvalues and eigenvectors.
  • Use Case: When analyzing the stability of a system or understanding the principal components of data, this skill helps compute the fundamental properties of matrices.

Quick Start

Use the eigenvalues skill to compute the eigenvalues for the matrix [[1,2],[3,4]].

Frequently Asked Questions about eigenvalues

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

FAQPage Schema
How do I compute eigenvalues and eigenvectors for a matrix using symbolic computation?▼

To compute eigenvalues and eigenvectors using symbolic computation, this Skill calculates the characteristic polynomial of a matrix and solves it using SymPy, then determines the corresponding eigenvectors automatically.

What is the characteristic polynomial and how is it used to find eigenvalues?▼

The characteristic polynomial is a polynomial equation derived from a square matrix that, when solved, yields the matrix's eigenvalues. This Skill computes it using SymPy for polynomial manipulation.

Can I verify computed eigenvalues and eigenvectors using automated proof tools?▼

Yes, you can verify computed eigenvalues and eigenvectors using automated proof tools. This Skill uses Z3 for logical verification to ensure the calculated eigenvalues and eigenvectors are mathematically correct.

Does SymPy support matrix computation for dynamic systems analysis and principal component analysis?▼

SymPy supports matrix computation for dynamic systems analysis and principal component analysis by calculating fundamental matrix properties. This Skill applies these computations to analyze system stability and data components.

What are the limitations of using symbolic math tools for eigenvalue calculation?▼

Limitations of using symbolic math tools for eigenvalue calculation include potential performance constraints with very large matrices, as solving characteristic polynomials symbolically can become computationally intensive.

Do I need Python and Z3 to calculate eigenvalues and verify linear algebra results?▼

Yes, you need Python scripts utilizing SymPy for polynomial manipulation and Z3 for logical verification to calculate eigenvalues and verify linear algebra results effectively.

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