---
id: lineax
version: "0.1.1"
license: Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. "License" shall mean the terms and conditions for… (full text in the JSON record)
license_treatment: permissive
maintenance: active
---

# lineax — Linear solvers in JAX and Equinox.

License: permissive · Maintenance: active · Downloads: 523.2K/mo

## What it is and what it does

Lineax is a JAX library for solving linear systems and least-squares problems, with support for both explicit matrices and implicit linear operators (e.g., Jacobians, transposes). It integrates with JAX's autodiff, autoparallelism, and GPU/TPU support, allowing you to differentiate through linear solves with numerically stable gradients. The library works with PyTree-valued matrices and vectors, and supports structured matrix types like symmetric matrices.

Typical use cases include solving Ax=b when A may be ill-posed or rectangular, computing least-squares solutions via QR or other solvers, and building implicit operators for problems where materializing the full matrix is infeasible or inefficient. It is part of the broader JAX ecosystem and depends on Equinox for PyTree utilities and jaxtyping for type annotations.

Use it for:

- Solve overdetermined or underdetermined linear systems without materializing the full matrix operator.
- Compute least-squares solutions with numerically stable gradients for optimization and inverse problems.
- Build implicit Jacobian and Hessian operators for Newton-like methods in scientific computing.
- Solve quadratic minimization problems by constructing a Hessian linear operator and solving the normal equations.
- Integrate linear solves into JAX-based neural network training pipelines with automatic differentiation.

## Worth the install?

AI-flagged interpretation of the facts above — verify before relying.

Lineax solves linear systems and least-squares problems in JAX, handling both explicit matrices and implicit linear operators without materializing them.

Yes, if you work in JAX and need linear solves or least-squares. The library is actively maintained, has low install friction, and integrates seamlessly with JAX's autodiff and GPU/TPU support. The Apache 2.0 license poses no restrictions. Alpha status (Development Status 3) means the API may change, but the package is in active use and well-documented.

## Install

pip install lineax
uv add lineax
poetry add lineax

## Installing lineax

Before you install: Low install friction with a pure-Python wheel. Actively maintained as of August 2026 with recent releases. Requires JAX 0.4.38+ and Equinox 0.11.10+, which are themselves substantial dependencies.

License in practice: Apache 2.0 permissive license allows commercial and derivative use with minimal restrictions—attribution and license notice required in distributions.

Quickstart:

pip install lineax

import jax.random as jr
import lineax as lx

matrix_key, vector_key = jr.split(jr.PRNGKey(0))
matrix = jr.normal(matrix_key, (10, 8))
vector = jr.normal(vector_key, (10,))
operator = lx.MatrixLinearOperator(matrix)
solution = lx.linear_solve(operator, vector, solver=lx.QR())

Requires Python 3.11+, JAX 0.4.38+, and Equinox 0.11.10+.

Verify before relying:

- Whether structured matrix support (e.g. symmetric) provides measurable performance gains in typical workflows.
- Stability and numerical accuracy of gradients through least-squares compared to alternative autodiff approaches.
- Performance characteristics of implicit operators on GPU/TPU relative to explicit matrix solves.

## Package facts

- License: Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. "License" shall mean the terms and conditions for… (full text in the JSON record) (permissive)
- Python support: supports_current
- Install friction: low
- Maintenance: active
- Downloads: 523.2K/month (top 15,000 on PyPI)
- Known vulnerabilities: none known

## Tags

jax linear solver, least squares solver jax, linear algebra jax, matrix equation solver, jax numerical linear algebra, implicit linear operators, qr solver jax, jax-ecosystem, numerical-methods, autodiff

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