How does the skill ensure the accuracy of the results?

It uses a 'Verify' step where it checks the Av = λv identity using Z3 to prove the correctness of the derived eigenvalues and eigenvectors.

Can this skill handle symbolic matrices?

Yes, the Sympy_Charpoly tool allows for computation using variables, such as calculating the characteristic polynomial of a matrix with variables a, b, c, and d.

What is the primary purpose of the Eigenvalues skill?

It provides a standardized workflow for Claude to solve linear algebra problems, specifically calculating and verifying eigenvalues and eigenvectors.

Which mathematical libraries does this skill utilize?

The skill leverages Sympy for symbolic computation and the Z3 theorem prover for formal verification of mathematical results.

Linear Algebra Eigenvalues

Name: Linear Algebra Eigenvalues
Author: parcadei

byparcadei

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3,382

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Data Science & ML

Solves complex linear algebra problems by calculating characteristic polynomials, eigenvalues, and eigenvectors using Sympy and Z3 verification.

This skill provides Claude with a specialized mathematical framework for solving eigenvalue problems in linear algebra. It streamlines the process of computing characteristic polynomials and finding exact eigenvalues and eigenvectors by leveraging symbolic computation via Sympy. To ensure mathematical rigor, the skill includes formal verification steps using the Z3 theorem prover, allowing users to prove matrix properties and verify algebraic or geometric multiplicities with high precision within their development environment.

Key Features

01Precise eigenvalue and eigenvector derivation using Sympy

02Structured decision tree for step-by-step matrix problem solving

03Automated characteristic polynomial computation for symbolic and numeric matrices

04Formal proof verification of Av = λv equations using Z3

053,382 GitHub stars

06Support for symbolic variables in matrix operations

Use Cases

01Implementing and debugging machine learning algorithms that rely on matrix transformations

02Verifying matrix stability and eigendecomposition for engineering and physics simulations

03Solving and verifying complex linear algebra problems in research or academic contexts

Key Features

01Precise eigenvalue and eigenvector derivation using Sympy

02Structured decision tree for step-by-step matrix problem solving

03Automated characteristic polynomial computation for symbolic and numeric matrices

04Formal proof verification of Av = λv equations using Z3

053,382 GitHub stars

06Support for symbolic variables in matrix operations

Use Cases

01Implementing and debugging machine learning algorithms that rely on matrix transformations

02Verifying matrix stability and eigendecomposition for engineering and physics simulations

03Solving and verifying complex linear algebra problems in research or academic contexts