skills.rest
scooter-lacroix
scooter-lacroixCOMMUNITY
Explore all skills by this author →
Website𝕏@scooter_lacroixGitHub

eigenvalues

Compute eigenvalues and eigenvectors for matrices using symbolic computation.

8|1|Updated Jan 4, 2026
Search Tags:#eigenvalues#linear algebra#sympy#symbolic math#eigenvectors#matrix computation
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill eigenvalues
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: eigenvalues
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/linear-algebra/eigenvalues
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill eigenvalues

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3-solver, and includes scripts (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 solvers to verify the computed eigenvalues and eigenvectors.
  • Use Case: When analyzing the stability of a system or understanding the principal components of data, you can use this skill to find the eigenvalues and eigenvectors of the system's matrix.

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 math?▼

Eigenvalues and eigenvectors are computed by solving the characteristic polynomial det(A - lambda*I) = 0. This skill automates matrix decomposition using symbolic computation, calculating the polynomial, solving for eigenvalues, and determining corresponding eigenvectors.

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

The characteristic polynomial is det(A - lambda*I) = 0, where A is a matrix and lambda represents eigenvalues. Solving this polynomial equation yields the eigenvalues, which are then used to calculate their corresponding eigenvectors for matrix decomposition analysis.

Can I use sympy for symbolic eigenvalue calculation and verify the results?▼

Yes, sympy performs the symbolic eigenvalue calculation, computing the characteristic polynomial and solving for eigenvalues and eigenvectors. The results are then verified using symbolic solvers to ensure accuracy of the computed matrix decomposition.

Does z3-solver work with sympy for verifying eigenvalue and eigenvector calculations?▼

Z3-solver is used alongside sympy to verify computed eigenvalues and eigenvectors. Sympy handles the symbolic matrix computation and characteristic polynomial solving, while z3-solver provides additional verification of the mathematical results.

When do I need eigenvalue and eigenvector calculations in linear algebra?▼

Eigenvalue and eigenvector calculations are needed for system stability analysis, understanding principal components in data science, and matrix decomposition tasks. They help analyze system dynamics and data structure by revealing fundamental properties of the transformation matrix.

What's the best way to calculate matrix eigenvalues for system dynamics analysis?▼

The best approach is using symbolic computation to solve the characteristic polynomial det(A - lambda*I) = 0. This skill automates the entire process from polynomial computation through eigenvalue extraction and eigenvector determination, with built-in verification for reliable results.

Related Skills

Explore More Software Engineering Skills→
scooter-lacroixscooter-lacroix
8

matrices

Solve matrix operations, linear systems, and decompositions with SymPy and Z3.

Community
Intermediate
parcadeiparcadei
3.9k

eigenvalues

Compute eigenvalues and eigenvectors using SymPy and verify with Z3.

Community
Intermediate
parcadeiparcadei
3.9k

matrices

Solves matrix problems in linear algebra using SymPy and Z3.

Community
Intermediate
ZurybrZurybr

largest-eigenval

Optimize largest eigenvalue computation for small dense matrices via Cython and LAPACK.

Community
Intermediate