# Linear Algebra

Matrix multiply, determinant, inverse, rank, linear solve, eigenvalues, vector ops, least squares and transforms.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://linear-algebra.x402tookit.com/openapi.json
- x402 manifest: https://linear-algebra.x402tookit.com/.well-known/x402
- Catalog (free): https://linear-algebra.x402tookit.com/catalog
- Health (free): https://linear-algebra.x402tookit.com/health
- Uptime (free): https://linear-algebra.x402tookit.com/uptime

## Endpoints (10)

### GET /determinant — $0.02
Determinant of a square matrix (up to 10x10) by LU with partial pivoting, flagging a numerically singular matrix.
Params: A: string
Example: https://linear-algebra.x402tookit.com/determinant?A=%5B%5B6%2C1%2C1%5D%2C%5B4%2C-2%2C5%5D%2C%5B2%2C8%2C7%5D%5D

### GET /eigen — $0.02
Eigenvalues and eigenvectors of a 2x2 matrix (closed form) or a symmetric matrix up to 10x10 (Jacobi).
Params: A: string
Example: https://linear-algebra.x402tookit.com/eigen?A=%5B%5B2%2C-1%2C0%5D%2C%5B-1%2C2%2C-1%5D%2C%5B0%2C-1%2C2%5D%5D

### GET /inverse — $0.02
Inverse of a square matrix (up to 10x10) by Gauss-Jordan, with A*inv(A) residual and a condition number.
Params: A: string
Example: https://linear-algebra.x402tookit.com/inverse?A=%5B%5B4%2C7%5D%2C%5B2%2C6%5D%5D

### GET /least-squares — $0.02
Least-squares line or polynomial fit (degree 1 to 6, up to 100 points) with coefficients, R-squared and residuals.
Params: x: string, y: string, degree?: integer, at?: number
Example: https://linear-algebra.x402tookit.com/least-squares?x=%5B1%2C2%2C3%2C4%5D&y=%5B6%2C5%2C7%2C10%5D&degree=1

### GET /matrix-multiply — $0.02
Multiply two matrices (up to 10x10) given as JSON, with shape check and the product matrix.
Params: A: string, B: string
Example: https://linear-algebra.x402tookit.com/matrix-multiply?A=%5B%5B1%2C2%5D%2C%5B3%2C4%5D%5D&B=%5B%5B5%2C6%5D%2C%5B7%2C8%5D%5D

### GET /rank — $0.02
Rank, nullity and reduced row echelon form of a matrix (up to 10x10) with pivot columns.
Params: A: string
Example: https://linear-algebra.x402tookit.com/rank?A=%5B%5B1%2C2%2C3%5D%2C%5B4%2C5%2C6%5D%2C%5B7%2C8%2C9%5D%5D

### GET /solve — $0.02
Solve Ax=b (n up to 10) by Gaussian elimination with partial pivoting; flags singular and ill-conditioned systems.
Params: A: string, b: string
Example: https://linear-algebra.x402tookit.com/solve?A=%5B%5B2%2C1%2C-1%5D%2C%5B-3%2C-1%2C2%5D%2C%5B-2%2C1%2C2%5D%5D&b=%5B8%2C-11%2C-3%5D

### GET /transform-compose — $0.02
Compose 2D or 3D rotate, scale and translate steps into one homogeneous matrix, optionally applied to a point.
Params: steps: string, dim?: integer, point?: string
Example: https://linear-algebra.x402tookit.com/transform-compose?steps=%5B%7B%22op%22%3A%22rotate%22%2C%22deg%22%3A90%7D%2C%7B%22op%22%3A%22translate%22%2C%22tx%22%3A1%2C%22ty%22%3A0%7D%5D&dim=2&point=%5B1%2C0%5D

### GET /transpose — $0.02
Transpose a matrix (up to 10x10) with trace, symmetry and skew-symmetry flags, and Frobenius and 1-norms.
Params: A: string
Example: https://linear-algebra.x402tookit.com/transpose?A=%5B%5B1%2C2%2C3%5D%2C%5B4%2C5%2C6%5D%5D

### GET /vector-ops — $0.02
Vector dot, cross, norm, angle, projection, unit vector and distance for vectors of up to 100 entries.
Params: op: string, a: string, b?: string
Example: https://linear-algebra.x402tookit.com/vector-ops?op=cross&a=%5B1%2C2%2C3%5D&b=%5B4%2C5%2C6%5D

## Terms

Educational numerical arithmetic computed locally on the numbers you supply, in 64-bit floating point, provided as is. Results carry rounding error, the condition number reported is what tells you how far to trust a solve or inverse, and rank and singularity are decided with a stated tolerance. Not engineering, safety or scientific certification.