# π About `eigenfind`
**`eigenfind`** is a lightweight Python library that allows you to compute **eigenvectors from known eigenvalues** of a square matrix β a task commonly needed in theoretical mathematics, linear algebra education, and symbolic or numerical analysis.
While most libraries like NumPy and SciPy compute eigenvalues and eigenvectors together, `eigenfind` fills a specific niche: solving the **eigenvalue problem in reverse** β finding eigenvectors **when you already know one or more eigenvalues**.
This is achieved by solving the homogeneous linear system:
$$
(A - \lambda I)\mathbf{v} = 0
$$
β¦which defines the eigenspace for a given eigenvalue `Ξ»` of matrix `A`.
---
## β
Key Features
* π Find eigenvectors corresponding to a **given eigenvalue**
* π Works with both **numeric** (NumPy/SciPy) and **symbolic** (SymPy) matrices
* π Educational use: ideal for students, educators, and math enthusiasts
* π§ Supports defective matrices (partial functionality)
* π§ͺ Easy to test and integrate into other math tools
---
## π§ Use Cases
* Teaching or learning linear algebra
* Verifying results from numerical solvers
* Debugging or inspecting eigenvalue computations
* Symbolic math derivations
* Building introspection tools for PCA or matrix decompositions
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