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Linear Algebra Eigenvalue & Eigenvector Calculator
x402
Linear Algebra Eigenvalue & Eigenvector Calculator is a paid API for AI agents from linear-algebra.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).
Computes eigenvalues and eigenvectors of a 2x2 matrix (closed-form) or a symmetric matrix up to 10x10 (Jacobi iteration), with spectral properties like trace, determinant, and definiteness.
Price / call$0.02
Success—
StatusUnknown
How this service works
Eigenvalues and eigenvectors of a 2x2 matrix (closed form) or a symmetric matrix up to 10x10 (Jacobi).
Output
Returns a JSON object containing eigenvalues (as objects with real 're' and imaginary 'im' parts), eigenvectors (as arrays of numbers), trace, determinant, sum and product of eigenvalues, definiteness classification, symmetry flag, the numerical method used (closed-form or Jacobi), max residual error (Av - λv), and any warnings about degraded or defective results.
Example use cases
Stability analysis of a dynamic system
“I have a 2x2 system matrix [[3,1],[0,2]] representing a linear dynamical system — can you compute its eigenvalues so I can check whether the system is stable?”
Positive definiteness check for optimization
“I need to verify that my 3x3 symmetric Hessian matrix [[4,1,0],[1,3,1],[0,1,5]] is positive definite — can you compute its eigenvalues and tell me the definiteness?”
PCA covariance matrix decomposition
“Can you find the eigenvalues and eigenvectors of this 4x4 symmetric covariance matrix [[2,1,0,0],[1,3,1,0],[0,1,2,1],[0,0,1,4]]? I need them for a principal component analysis.”
Technical details
Endpoint
GEThttps://linear-algebra.x402tookit.com/eigen?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need eigenvalues and eigenvectors with full spectral metadata (definiteness, trace, determinant, residual) for a 2x2 matrix or a symmetric matrix up to 10x10. Prefer it over general-purpose CAS tools when you want a lightweight, pay-per-call computation with numerical reliability checks and Jacobi-method accuracy reporting built in.
Side effects
- Non-symmetric matrix larger than 2x2 may be rejected or flagged — only symmetric matrices up to 10x10 are supported beyond 2x2
- Malformed matrix input (non-square, wrong JSON format) returns an error
- Matrix exceeding 10x10 is rejected
- Numerically ill-conditioned or near-defective matrices may return degraded results with a warning flag
- Complex eigenvalues for non-symmetric 2x2 inputs are returned with non-zero imaginary parts
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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